CECW-EG

Engineer Manual

1110-2-1901

Department of the Army

U.S. Army Corps of Engineers

Washington, DC 20314-1000

EM 1110-2-1901

30 September 1986

(original)

 30 April 1993

(change 1)

Engineering and Design

SEEPAGE ANALYSIS AND

CONTROL FOR DAMS

Distribution Restriction Statement

Approved for public release;

distribution is unlimited.
CECW-EG-8 

Engineer Manual 

No. 1110-2-1901 

DEPARTMENT OF THE ARMY 

U.S. Army Corps of Engineers 

Washington, DC 20314-1000 

Engineering and Design 

SEEPAGE ANALYSIS AND CONTROL FOR DAMS 

EM 1110-2-1901 

Change 1 

30 April 1993 

1. This change replaces Appendix D, "Filter and Drain Design and Construction" of EM 1110-2-1901, 

dated 30 September 1986. 

2. File this change sheet in front of the publication for reference purposes. 

FOR TilE COMMANDER: 

WILUAM D. BROWN 

Colonel, Corps of Engineers 

Chief of Staff 
ENGINEER MANUAL EM 1110-2-1901

30 September 1986

ENGINEERING AND DESIGN

SEEPAGE ANALYSIS AND

CONTROL FOR DAMS

DEPARTMENT OF THE ARMY

CORPS OF ENGINEERS

OFFICE OF THE CHIEF OF ENGINEERS
DAEN-ECE-G

Engineer Manual

No. 1110-2-1901

30 September 1986

Engineering and Design

SEEPAGE ANALYSIS AND CONTROL FOR DAMS

1. Purpose. This manual presents the fundamental design principles and

guidance concerning seepage considerations for design of new dams and the

evaluation of existing projects.

2. Applicability. This manual is applicable to all HQUSACE/OCE elements and

field operating activities having responsibility for the design and

construction of civil works projects.

3. Discussion. All earth and rock-fill dams are subject to seepage through

the embankment, foundation, and abutments. Concrete gravity and arch dams are

subject to seepage through the foundation and abutments. Seepage control is

necessary to prevent excessive uplift pressures, sloughing of the downstream

slope, piping through the embankment and foundation, and erosion of material

by loss into open joints in the foundation and abutments. The purpose of the

project, i.e., long-term storage, flood control, etc., may impose limitations

on the allowable quantity of seepage.

FOR THE COMMANDER:

Chief of Staff

This manual supersedes EM 1110-2-1901 dated February 1952
DEPARTMENT OF THE ARMY

US Army Corps of Engineers

Washington, D. C. 20314-1000

EM-1110-2-1901

30 September 1986

DAEN-ECE-G

Engineer Manual

No. 1110-2-1901

Engineering and Design

SEEPAGE ANALYSIS AND CONTROL FOR DAMS

Table of Contents

Subject Paragraph Page

CHAPTER 1. INTRODUCTION

Purpose------------------------------------

Applicability------------------------------

References---------------------------------

Objective and Scope------------------------

General Considerations---------------------

1-1

1-2

1-3

1-4

1-5

1-1

1-1

1-1

1-1

1-1

CHAPTER 2. DETERMINATION OF PERMEABILITY OF SOIL

AND CHEMICAL COMPOSITION OF WATER

Darcy's Law--------------------------------

Range of Validity of Darcy's Law-----------

Coefficient of Permeability----------------

Factors Influencing Permeability-----------

Indirect Methods for Determining

Permeability-----------------------------

Laboratory Methods for Determining

Permeability-----------------------------

Origin, Occurrence, and Movement of

Ground Water-----------------------------

Field Methods for Determining

permeability-----------------------------

Chemical Composition of Ground Water and

River (or Reservoir) Water---------------

2-1 2-1

2-2 2-4

2-3 2-6

2-4 2-9

2-5 2-20

2-6 2-28

2-7 2-30

2-8 2-33

2-9 2-34

CHAPTER 3. DETERMINATION OF PERMEABILITY OF ROCK

Permeabilities of Rock Masses--------------

Flow Characteristics in Rock Masses--------

Methods for Determining Rock Mass

Permeability-----------------------------

Applications of Rock Mass Permeability-----

3-1 3-1

3-2 3-1

3-3

3-4

3-3

3-11

This manual supersedes EM 1110-2-1901, Feb 52

i
EM 1110-2-1901

30 Sep 86

Subject Paragraph Page

CHAPTER 4. SEEPAGE PRINCIPLES

General Considerations----------------------

Boundary Conditions-------------------------

Confined and Unconfined Flow Problems-------

Laplace’s Equation------------------------

Methods for Solution of Laplace's

Equation------------------------------

Graphical Method for Flow Net

Construction-----------------------------

Flow Net for Anisotropic Soil---------------

Flow Net for Composite Sections-------------

Determination of Seepage Quantities,

Escape Gradients, Seepage Forces, and

Uplift Pressures--------------------------

4-1 4-1

4-2 4-1

4-3 4-2

4-4 4-3

4-5

4-6

4-7

4-8

4-5

4-9

4-14

4-14

4-9 4-21

CHAPTER 5. CONFINED FLOW PROBLEMS

General Considerations----------------------

Gravity Dam on Pervious Foundation of

Finite Depth------------------------------

Gravity Dams on Infinitely Deep

Pervious Foundations------------------------

5-1 5-1

5-2 5-1

5-3 5-1

CHAPTER 6. UNCONFINED FLOW PROBLEMS

Introduction --------------------------------

Homogeneous Earth Dam on Impervious

Foundation --------------------------------

Earth Dam with Horizontal Drain on

Impervious Foundation---------------------

Earth Dam with Toe Drain on Impervious

Foundation --------------------------------

Earth Dam with Vertical or near Vertical

Horizontal Drains on Impervious

Foundation--------------------------------

Flow Net for a Composite Zoned Dam----------

Zoned Earth Dam on Pervious Foundation------

6-1 6-1

6-2 6-1

6-3 6-10

6-4 6-10

6-5 6-10

6-6 6-10

6-7 6-17

CHAPTER 7. SEEPAGE TOWARD WELLS

Use of Wells--------------------------------

Analysis of Well Problems-------------------

Basic Well Equations for Steady State

Flow--------------------------------------

Special Conditions--------------------------

Nonsteady State Flow------------------------

7-1 7-1

7-2 7-1

7-3 7-2

7-4 7-11

7-5 7-21

ii
EM 1110-2-1901

30 Sep 86

Subject Paragraph Page

CHAPTER 8. SEEPAGE CONTROL IN EMBANKMENTS

CHAPTER 9. SEEPAGE CONTROL IN EARTH FOUNDATIONS

CHAPTER 10.

CHAPTER 11.

CHAPTER 12. REMEDIAL SEEPAGE CONTROL

General-------------------------------------

Methods for Seepage Control-----------------

Flat Slopes Without Drains------------------

Zoning Embankments--------------------------

Vertical (or Inclined) and Horizontal

Drains------------------------------------

Seepage Control Against Earthquake

8-1

8-2

8-3

8-4

8-5

8-6

8-1

8-1

8-1

8-1

Effects-----------------------------------

8-8

8-18

General-------------------------------------

Selection of Method for Seepage

9-1

9-2

9-3

9-4

9-5

9-6

9-7

9-8

9-9

9-1

Control -----------------------------------

Horizontal Drains---------------------------

Cutoffs-------------------------------------

Upstream Impervious Blanket-----------------

Downstream Seepage Berms--------------------

Relief Wells--------------------------------

Trench Drain--------------------------------

Concrete Galleries--------------------------

9-1

9-1

9-1

9-48

9-58

9-62

9-83

9-84

SEEPAGE CONTROL THROUGH EARTH ABUTMENTS

ADJACENT TO STRUCTURES AND BENEATH

SPILLWAYS AND STILLING BASINS

Through Earth Abutments---------------------

Adjacent to Outlet Conduits-----------------

Beneath Spillways and Stilling Basins-------

10-1

10-2

10-3

10-1

10-1

10-3

SEEPAGE CONTROL IN ROCK FOUNDATIONS AND

ABUTMENTS

General Considerations----------------------

Cutoff Trenches-----------------------------

Abutment Impervious Blankets----------------

Drainage and Grouting Galleries and

Tunnels-----------------------------------

Grouting of Foundations and Abutments-------

Surface Treatment of Foundations and

Abutments---------------------------------

11-1

11-2

11-3

11-1

11-1

11-2

11-4

11-5

11-2

11-3

11-6 11-3

General Considerations---------------------- 12-1 12-1

Remedial Methods---------------------------- 12-2 12-1

Storage Restriction------------------------- 12-3 12-2

Grouting ------------------------------------ 12-4 12-2

iii
EM 1110-2-1901

30 Sep 86

Subject

CHAPTER 13.

CHAPTER 14.

APPENDIX A.

APPENDIX B.

APPENDIX C.

Upstream Impervious Blanket----------------- 12-5

Downstream Berm----------------------------- 12-6

Slurry Trench Cutoff------------------------ 12-7

Relief Wells-------------------------------- 12-8

Drainage of Downstream Slope---------------- 12-9

Page

12-4

12-6

12-6

12-11

12-12

MONITORING PERFORMANCE OF SEEPAGE CONTROL

MEASURES

General Considerations---------------------- 13-1 13-1

Piezometers for Seepage Pressures----------- 13-2 13-1

Flow Measurements--------------------------- 13-3 13-12

Seepage Water Analysis---------------------- 13-4 13-18

Remote Sensing Methods---------------------- 13-5 13-20

INSPECTION, MAINTENANCE, AND REHABILITATION OF SEEPAGE CONTROL MEASURES

Introduction -------------------------------- 14-1 14-1

Inspection---------------------------------- 14-2 14-1

Maintenance--------------------------------- 14-3 14-1

Rehabilitation------------------------------ 14-4 14-3

REFERENCES

Government Publications---------------------

Non-Government Publications-----------------

APPROXIMATE METHODS FOR ANALYSIS OF FLOW

PROBLEMS

A-1

A-11

Introduction--------------------------------

Electrical Analogy--------------------------

Sand Tank Model-----------------------------

Viscous Flow Models-------------------------

Method of Fragments-------------------------

Finite Difference Method--------------------

Finite Element Method-----------------------

B-1 B-1

B-2 B-1

B-3 B-2

B-4 B-5

B-5 B-5

B-6 B-28

B-7 B-29

ANALYSIS OF PRESSURE INJECTION TESTS

(Ziegler 1976)

Water pressure Tests------------------------

Air pressure Tests--------------------------

pressure Holding Testy----------------------

C-1

C-2

C-3

C-1

C-11

C-17

Paragraph

iv
EM 1110-2-1901

30 Sep 86

Subject Paragraph Page

APPENDIX D. FILTER AND DRAIN DESIGN AND CONSTRUCTION

General---------------------------------------

Stability-------------------------------------

Permeability----------------------------------

Applicability---------------------------------

Perforated Pipe---------------------------

Gap-Graded Base---------------------------

Gap-Graded Filter-------------------------

Broadly-Graded Base-----------------------

Graded Filter Design----------------------

Geotextiles-----------------------------------

Construction----------------------------------

Monitoring------------------------------------

D-1

D-2

D-3

D-4

D-5

D-6

D-7

D-8

D-9

D-10

D-11

D-12

D-1

D-1

D-2

D-2

D-3

D-3

D-5

D-5

D-5

D-6

D-6

D-8

v
EM 1110-2-1901

30 Sep 86

CHAPTER 1

INTRODUCTION

1-1. Purpose. This manual provides guidance and information concerning seepage analysis and control for dams.

1-2. Applicability. The provisions of this manual are applicable to all

HQUSACE/OCE elements and field operating activities (FOA) having responsibility for seepage analysis and control for dams.

1-3 References. Appendix A contains a list of Government and non-Government

references pertaining to this manual. Each reference is identified in the

text by either the designated publication number or by author and date.

Reference to cited material in tables and figures is identified throughout the

manual by superscripted numbers (item 1, 2, etc.) that correspond to similarly

numbered items in Appendix A.

1-4. Objective and Scope. The objective of this manual is to provide a guide

for seepage analysis and control for dams.

1-5. General Considerations. All earth and rock-fill dams are subject to

seepage through the embankment, foundation, and abutments. Concrete gravity

and arch dams are subject to seepage through the foundation and abutments.

Seepage control is necessary to prevent excessive uplift pressures, sloughing

of the downstream slope, piping through the embankment and foundation, and

erosion of material by loss into open joints in the foundation and abutments.

The purpose of the project, i.e., long-term storage, flood control, etc., may

impose limitations on the allowable quantity of seepage (Sowers 1977).

1-1
EM 1110-2-1901

30 Sep 86

CHAPTER 2

DETERMINATION OF PERMEABILITY OF SOIL AND

CHEMICAL COMPOSITION OF WATER

2-1. Darcy's Law.

a. Development of Darcy's Law. Henry Darcy, a French engineer, conducted a laboratory experiment to study the flow of water in verticals and

filters which he published in his 1856 treatise. The results of his experiment

indicated that (Rouse and Ince 1957)

v = ki (2-1)

or since Q = VA

or using q =

Q = kiAt

q = kiA

(2-2)

(2-3)

\where

v = discharge velocity

k = (1) Darcy's coefficient of permeability

i = hydraulic gradient (head loss/length over which head loss occurs)

Q = quantity of discharge

A = cross-sectional area of flow

t = time of flow

q = rate of discharge

b. Extension to Inclined Soil Column. Darcy's law may be extended to

flow through an inclined soil column given in figure 2-1 (Harr 1962). As

indicated in equation 2-1, flow is a consequence of differences in total

(1) Commonly called the coefficient of permeability or the permeability.

2-1
EM 1110-2-1901

30 Sep 86

head(l) and not of pressure gradients (Harr 1962 and Bear 1972). As shown in

figure 2-1, flow is directed from point A to point B even though the pressure

at point B is greater than that at point A.

Figure 2-1. Darcy's law for flow through inclined soil column

(prepared by WES)

(1) The elevation head at any point is the distance from some arbitrary datum.

The pressure head is the water pressure divided by the unit weight of the

water. The total head is the sum of the elevation head and the pressure

head.

2-2
EM 1110-2-1901

30 Sep 86

c. Discharge Velocity and Seepage Velocity. The discharge velocity is

defined as the quantity of fluid that flows through a unit cross-sectional area

of the soil oriented at a right angle to the direction of flow in a unit time.

The discharge velocity is used in determining the quantity of flow or rate of

discharge through a soil. As flow can occur only through the interconnected

pores of the soil, as shown in figure 2-2, the actual rate of

Figure 2-2. Concepts of flow paths through a soil column

(prepared by WES)

movement of the water, as measured with dye tracers for instance, is the seepage velocity (Harr 1962 and Casagrande 1937) which exceeds the discharge

velocity.

2-3

(2-4)
EM 1110-2-1901

30 Sep 86

where

seepage velocity

n = porosity (ratio of volume of voids to the total volume of the soil

mass)

It follows that

Equation 2-5 is a useful expression in estimating field permeabilities using

dye tracers (Soil Conservation Service 1978).

2-2. Range of Validity of Darcy's Law.

a. Lower Bound. Darcy's law (equations 2-1 through 2-3) applies to

linear flow (adjacent flow lines are locally straight and parallel). For flows

through soils, there are two situations where the validity of this linear

relationship may not hold. For highly plastic clays of low permeability, there

may be a threshold hydraulic gradient below which flow does not take place.

Such conditions may occur in deeply buried clays and clay shales. For many

practical seepage problems the rate of flow through these soil layers is so

small that they can be considered to be impervious (Mitchell 1976, Chugaev

1971, Basak and Madhav 1979, and Muskat 1946).

b. Upper Bound. Of greater practical importance is the upper limit on

the range of validity of Darcy's law. It has been recognized that, at very

high flow rates, Darcy's law does not hold (Chugaev 1971). The upper limit is

usually identified using Reynolds number, a dimensionless number that expresses

the ratio of internal to viscous forces during flow. It is often used in fluid

mechanics to distinguish between laminar flow (fluid layer flows alongside of

another at approximately the same velocity with no macroscopic mixing of fluid

particles) at low velocities and turbulent flow (velocity fluctuations, both

parallel and transverse, are imposed upon the mean motion with mixing of the

fluid particles) at high velocities. The Reynolds number for flow through

soils is

(2-6)

where

Reynolds number

D = average diameter of soil particles

2-4
EM 1110-2-1901

30 Sep 86

= density of fluid

= coefficient of dynamic viscosity of fluid

The critical value-of Reynolds number at which the flow in soils changes from

laminar to turbulent has been determined experimentally by various investigators to range from 1 to 12 (Harr 1962 and Chugaev 1971). Assuming a water

temperature of 20o C, substituting = 998.2 kg/m3 and μ = 1.002 x 10-3

kg/m

sec into equation 2-6, and assuming values of D and solving for v with

= 1 and = 12 gives the relationship shown in figure 2-3 which defines

the upper bound of the validity of Darcy's law. Depending on the discharge

velocity, Darcy's law is generally applicable for silts through medium sands.

c. Turbulent Flow.

(1) Estimating Permeability from Empirical Equation. For flow through

soils more pervious than medium sands, flow is likely to be turbulent. Under

turbulent conditions, the seepage velocity in a material with monosized soil

particles (coarse sands and/or gravels) can be estimated from the following

equation (Wilkins 1956, Leps 1973, and Stephenson 1979).

(2-7)

where

= seepage velocity in inches per second

w = an empirical constant, which depends on the shape and roughness of

the soil particles and viscosity of water and varies from 33 for

crushed gravel to 46 for polished marbles, in inch 1/2 per second

M = hydraulic mean radius of the rock voids (for a given volume of

particles equal to the volume of voids divided by the total surface

area of the particles, or the void ratio divided by the surface area

per unit volume of solids) in inches

i = hydraulic gradient

The coefficient of permeability is obtained from the seepage velocity using

equation 2-5. For well-graded soils, the D50 size (50 percent finer by weight)

can be used to calculate the hydraulic mean radius provided that the minus

1-in.-size material is less than 30 percent by weight. If there is more than

30 percent of minus 1-in .-size material, the permeability should be determined

experimentally (Leps 1973).

(2) Determining Permeability Experimentally. Alternatively, for flow

through soils more pervious than medium sands, the relationship between

hydraulic gradient and discharge velocity can be determined experimentally

(Cedergren 1977).

2-5
EM 1110-2-1901

30 Sep 86

Figure 2-3. Boundary between laminar and turbulent flow determined

using Reynolds number for temperature of 20° C (prepared by WES)

2-3. Coefficient of Permeability.

a. Darcy's (Engineer's) Coefficient of Permeability. The coefficient

of permeability used in seepage analysis for dams is called the Darcy's or

engineer's coefficient and is given by (Cedergren 1977)

2-6
EM 1110-2-1901

30 Sep 86

(2-8)

or since Q = VA

or using q =

(2-9)

(2-10)

The coefficient of permeability is defined as the rate of discharge-of water

at a temperature of 20o C under conditions of laminar flow through a unit

cross-sectional area of a saturated soil medium. The coefficient of permeability has the dimensions of a velocity and is usually expressed in centimeters per second. Permeability computed on the basis of Darcy's law is

limited to the conditions of laminar flow and complete saturation of the soil.

Under conditions of partial saturation, the flow is in a transient state and

is time dependent. To analyze natural flow conditions which depart from the

Darcy flow condition, it is sometimes necessary to apply Darcy's law in conditions where it is not strictly valid. When this is done, the effects of turbulent flow and partial saturation on the permeability must be recognized and

taken into consideration (Cedergren 1975).

b. Intrinsic (Specific) Permeability. The coefficient of permeability

of a soil material varies for different pore fluids depending upon their

density and viscosity as follows:

where

= intrinsic permeability

= unit weight of pore fluid

μ = viscosity of pore fluid

(2-11)

The intrinsic permeability has the dimensions of length squared and is

expressed in square centimeters or Darcy's (equal to 1.01 x 10-8 cm

2

). Figure 2-4 is a chart for the conversion of permeability values from one set of

2-7
2-8

10-5 w-6 

__ 

1ol 102 10 10-1 

1-- High -4)+1 <<----Medium ----k----- Low -----*<----Very low----k-----Practically imp

• For water at 2o•c 

Figure 2-4. 

To convert from em/sec to: 

Multiply by: 

m/min 

0.600 

JJ/sec 

104 

ft/sec 

0.0328 

ft/min ft/yr 

1.968 1.034 )( 106 

Permeability conversion chart (courtesy of John Wiley & Sons, In
EM 1110-2-1901

30 Sep 86

units to another (Lohman et al. 1972). Substituting equation 2-11 into

equation 2-1

(2-12)

Equation 2-12 may be used when dealing with more than one fluid or with temperature variations. This is widely used in the petroleum industry where the

presence of gas, oil, and water occur in multiphase flow systems (Freeze and

Cherry 1979, and Bureau of Reclamation 1977). In seepage analysis for earth

dams where we are primarily interested in the flow of water subject to small

changes in temperature, this refinement is seldom required.

c. Transmissivity Factor. In order to describe the flow characteristics of an aquifer (saturated permeable geologic unit that can transmit

significant quantities of water under ordinary hydraulic gradients),

C. V. Thesis introduced the term transmissivity which is defined as (Bureau of

Reclamation 1977)

T = kt (2-13)

where

T = transmissivity factor

k = average permeability

t = aquifer thickness

Transmissivity represents the rate of discharge for a gradient of unity

through a vertical strip of aquifer one unit wide and has dimensions of length

squared per unit time and is usually expressed in square feet per day.

2-4. Factors Influencing Permeability.

a. Range of Values of Permeability. No other property of soil exhibits

a wider range of values (up to ten orders of magnitude) or shows greater

directional (anisotropy) and spatial variability in a given deposit as does

the coefficient of permeability. The approximate range in coefficients of

permeability for soils and rocks is shown in figure 2-5 (Milligan 1976).

Within the range, extreme variations of permeability in situ are possible due

to the degree of stratification or heterogeneity of the soil deposit.

b. Variation of In Situ Permeability. Natural soil deposits are

generally stratified in structure. Water-deposited soils are laid down in

'horizontal layers and are often more permeable in the horizontal than vertical

direction. Windblown sands and silts are generally more permeable vertically

than horizontally due to the presence of continuous vertical root holes. An

important example of stratification is openwork gravel which may occur in

2-9
EM 1110-2-1901

30 Sep 86

Figure 2-5. Approximate range in coefficient of

permeability of soils and rocks (from Milligan224

)

ordinary gravel or soil and have tremendous influence on the watertightness of

dam foundations and abutments as shown in figure 2-6 (Cedergren 1977). Figure 2-6a shows a soil profile surmised from several drill holes. The grain

size analysis of soil samples taken at frequent intervals erroneously indicated

that the deposit was composed of relatively uniform sandy gravels. Laboratory

permeability tests on disturbed samples produced coefficients of permeability

of about 1 x 10-6 cm/sec. Using this value of permeability, the probable

seepage loss beneath the proposed dam was estimated to be 3 cu ft/day, which is

an insignificant quantity. However, the design engineer had observed many

openwork streaks in which the fines fraction of the material was almost

completely absent along the banks of the river and noted that the ground-water

table was level for several hundred feet away from the river and fluctuated

rapidly with changes in river stage. Field pumping tests were conducted which

indicated somewhat variable permeabilities but none approaching the magnitude

of openwork gravels. Based upon the available data, the dam was designed with

a cutoff trench to bedrock. During the excavation of the cutoff trench,

streaks of openwork gravel were found throughout the foundation. A revised

seepage computation based on a permeability of 30 cm/sec indicated that without

the cutoff trench, the theoretical underseepage would be about 1,000,000 cu

ft/day. If openwork gravel or other important discontinuities in earth dam

foundations remain undetected, serious problems from excessive seepage and

hydrostatic pressures will develop. This example illustrates the potential

serious effects of deviations between the design assumptions and the as-built

dam (Cedergren 1977). Also, thin continuous seams of cohesive soil can

drastically alter the vertical flow through what would otherwise be a highly

permeable site.

2-10
EM 1110-2-1901

30 Sep 86

a. Soil profile surmised from

drill holes with estimated

quantity of seepage under

dam equal to 3 cu ft/day

b. Soil profile revealed by

cutoff trench with estimated quantity of seepage under dam equal to

1,000,000 cu ft/day

(without cutoff trench)

Figure 2-6. Influence of openwork gravel on underseepage

(courtesy of John Wiley & Sons, Inc. 155)

c. Properties of the Seepage Fluid. The

fluid which influence the permeability of soils

viscosity, and chemical composition.

(1) As shown in table 2-1, for the range

properties of the seepage

are the temperature, density,

of temperatures ordinarily

encountered in seepage analysis of dams (0o C to 40o C) the density of water

is nearly constant (varies less than 1 percent).

Table 2-1. Properties of Watera

Temperature

°C oF

Density Viscosity

kg/m3

kg/m sec

0 32 999.8 1.787

5 41 999.9 1.519

10 50 999.7 1.307

15 59 999.1 1.139

20 68 998.2 1.002

25 77 997.0 0.890

30 86 995.6 0.798

35 95 994.0 0.719

40 104 992.2 0.653

x 10-3

a

Prepared by WES.

2-11
EM 1110-2-1901

30 Sep 86

(2) The viscosity varies up to 63.5 percent over the range of temperatures ordinarily encountered in seepage analysis of dams. As indicated in

equation 2-11, the permeability is inversely proportional to the viscosity of

the water. As given in table 2-1, the viscosity of water decreases as temperature increases. Therefore, the coefficient of permeability of the soil

increases as the temperature of the water increases. Permeability tests are

run at the most convenient temperature and reported at 20o C.

(3) The total dissolved salts (TDS) present in the seepage water may

influence the permeability of the soil, particularly for cohesive soils (Quirk

and Schofield 1955 and Cary, Walter, and Harstad 1943). Available data indicate that cohesive soils may be two to three orders of magnitude more permeable

to seepage water containing moderate amounts of dissolved salts (less than

300 parts per million by weight) than the distilled water (Carry, Walter, and

Harstad 1943).

d. Degree of Saturation. The degree of saturation of a soil

where

S = degree of saturation

(2-14)

= volume of water

Vv = volume of voids

has an important influence on permeability. A decrease in the degree of

saturation causes a decrease in the permeability as shown in figure 2-7 (Lambe

1951). When the degree of saturation is less than 85 percent, much of the air

would be continuous throughout the soil voids and Darcy's law would not hold.

When the degree of saturation is greater than 85 percent, most of air present

in the soil is in the form of small occluded bubbles and Darcy's law will be

approximately valid. The ratio of the permeability of the unsaturated sand to

the saturated sand at the same void ratio is given as (Scott 1963 and Parker

and Thornton 1976)

where

k

us

= unsaturated permeability

m = constant with values between 2 (uniform grain size) and

4 (well-graded materials)

(2-15)

2-12
EM 1110-2-1901

30 Sep 86

Figure 2-7. Permeability versus degree of saturation for

various sands (courtesy of John Wiley & Sons, Inc. 200)

e. Hydraulic Gradient. The hydraulic gradient

(2-16)

where

H = head loss

L = length over which head loss occurs

2-13
EM 1110-2-1901

30 Sep 86

at which permeability is measured can have a significant influence on the

coefficient of permeability computed from Darcy's law under certain conditions. The maximum hydraulic gradient for which laminar flow occurs for a

particular soil at a given density may be determined in the laboratory by

plotting the discharge velocity

(2-17)

versus the hydraulic gradient as shown in figure 2-8. A straight line

relationship indicates laminar flow

(2-18)

while deviations from the straight line at high gradients indicate turbulent

flow. Darcy's law for a fine sand, as shown in figure 2-8, is valid only for

the hydraulic gradient less than 2 for the loose state and 4.5 for the dense

state. For soils larger than a fine sand, Darcy's law is valid for progressively smaller hydraulic gradients (Burmister 1948 and Burmister 1955).

f. Particle Size. For cohesive soils, the permeability increases with

increases in clay mineral size and increase in void ratio (ratio of the volume

of voids to the volume of solid particles in the soil mass) as shown in

figure 2-9 (Yong and Warkentin 1966).(l) For cohesionless soils, the size and

shape of the soil particles influence the permeability. Allan Hazan conducted

tests on filter sands for use in waterworks and found that for uniform loose

clean sands the permeability was given by (Taylor 1948)

(2-19)

where

k - coefficient of permeability in cm per second

D 1 0 = particle size in cm at which 10 percent of the material is finer

by weight (also known as Hazen's effective size)

(1) As shown in table 2-2, the exchangeable cation present influences the

permeability of clay minerals at constant void ratio (Scott 1963). The

permeabilities are much smaller when the exchangeable cation is sodium

which is one of the reasons why sodium montmorillonite is used to seal

reservoirs.

2-14
EM 1110-2-1901

30 Sep 86

Figure 2-8. Determination of maximum hydraulic gradient for

which laminar flow occurs for a fine sand (courtesy of

American Society for Testing and Materials 147 )

Hazen's experiments were made on sands for which 0.1 mm < D10 < 0.3 mm and the

uniformity coefficient, Cu < 5 , where

where

Cu

= uniformity coefficient

D6 0 = particle size at which 60 percent of the material is finer by

weight

(2-20)

The coefficient 100 is an average of many values which ranged from 41 to 146,

but most of the values were from 81 to 117. Equation 2-19 makes no allowance

for variations in shape of the soil particles or void ratio.

2-15
EM 1110-2-1901

30 Sep 86

a. Edge view sketch to show relative

size and shape of clay particles

(dimension not shown in length)

b. Permeability versus void ratio for various

clay minerals

Figure 2-9. Influence of particle size and void ratio on

permeability of clay minerals (courtesy of Macmillan294)

2-16
EM 1110-2-1901

30 Sep 86

Table 2-2. Coefficients of Permeability for Different Exchange

Cations and Void Ratios for Two Clay Mineralsa

Permeabilities are obtained by falling-head test on samples in consolidation

apparatus. Results indicate the following:

For montmorillonite at void ratio 8 the order of permeability in terms of

the exchangeable ion present is

for kaolinite at void ratio 1.5 the order is

For compacted soils it is also observed that the permeability is much lower

(x 10-l to 10-2) in soils compacted slightly wet of optimum than in soils

compacted dry of optimum; it is thought that this occurs because of the

parallel arrangement of clay platelets in the wetter material after

compaction.

a

Courtesy of Addison-Wesley Publishing Company, Inc. 251

.

2-17
EM 1110-2-1901

30 Sep 86

g. Particle Shape and Surface Roughness. Cohesionless soil particles

have different particle shapes and surface roughness dependent on the distance

they have been transported by flowing water from the place of original erosion. As shown in table 2-3, the measured permeability is several orders of

magnitude lower for angular sand particles with rough surfaces than for

rounded sand particles with smooth surfaces (Burmister 1948). For uniform

cohesionless soils, crushing of particles during compaction with resulting

decrease in permeability occurs to a higher degree in soils with angular

shapes and rough surfaces than in soils with rounded shapes and smooth surfaces. Crushing of particles during compaction leads to an increase in the

amount of silt-sized particles (smaller than No. 200 sieve or 0.074 mm) which

results in lower permeability. For this and other reasons (cementation in

limestones and arching due to particle angularity) crushed rock is generally

not used for filters in earth dams. Also, table 2-3 compares the measured

permeability with the permeability computed from equation 2-19 developed by

Hazen for uniform loose clean sands. The agreement between measured and

computed permeability is within one order of magnitude for uniform sands and

glass spheres. Therefore, Hazen's equation should be used only for uniform

sands (sphericity and roundness > 0.90). The sphericity and roundness may be

estimated for sands using figure 2-10 (Krumbein and Sloss 1951).

h. Void Ratio. The permeability increases as the void ratio increases.

(2-21)

where

e = void ratio

Vs = volume of solids

There are considerable laboratory test data, shown in figure 2-11, which

indicate that a plot of void ratio versus log of coefficient of permeability

is frequently a straight line (Lambe and Whitman 1969).

i. Amount and Type of Fines Present. The permeability of sands and

gravels varies significantly with the amount and type of fines (material

smaller than the No. 200 sieve) (Barber and Sawyer 1952; Fenn 1966; Younger

and Lim 1972; Strohm, Nettles, and Calhoun 1967; Nettles and Calhoun 1967, and

Loudon 1952). As shown in figure 2-12a, the addition of 2.5 percent, by dry

weight, silt fines to concrete sand results in an order of magnitude decrease

in permeability (Barber and Sawyer 1952). The addition of 6.5 percent silt

fines to concrete sand decreases the permeability two orders of magnitude.

Similar results are obtained by the addition of somewhat larger amounts of clay

and limestone fines to concrete sand. As shown in figure 2-12b, the addition

of 2.0 percent silt fines to a sand-gravel mixture results in an order of

magnitude decrease in permeability (Barber and Sawyer 1952). The addition of

4.2 percent silt fines to sand-gravel mixture decreases the permeability

two orders of magnitude. Similar results are obtained by the addition of

2-18
2-19

Table 2-3. Influence of Particle Shape and Surface Roughness on 

Surface 

of Material Rouahness 

Crushed Sudeten granite Very rough 0.68 

Nysd Klodzkd River sand Very rough 0.75 

Odra River sand Rough to smooth 0.84 Odra River sand Rough to smooth 0.87 

Baltic Beach sand Smooth 0.87 

Glass spheres Very smooth 1.00 

(!)Courtesy of British Geotechnical Society146 

{2) 

(3) 

c 

c 0 10 X 060 

(4) k • 100 D10 • 

c<2) cO> Void 

Roundness _ u_ _c _ Ratio 

0.10 3.09 I. 54 0.543 

o. 15 5.47 2.20 0.451 

0.55 2.58 0.87 0.595 0.65 2.42 0.83 0.608 

0.85 I. 91 0.89 0.720 

1.00 I. 38 0.92 0.691 

Permeability of Sand(l) 

Relative Coefficient o

Density e

Measured 

79 5.00 X 10-5 

79 5.19 X 10-6 

58 9.41 X 10-4 

63 5.44 X 10-3 

38 1.83 X 10-3 

67 6.45 X 10-J 
EN 1110-2-1901

30 Sep 86

Figure 2-10. Krumbein and Sloss standard chart for

visual estimation of sphericity and roundness of

cohesionless soils (courtesy of W. H. Freeman

and Company 198)

somewhat smaller amounts of clay and larger amounts of limestone, respectively, to a sand-gravel mixture. As shown in figure 2-12c, the addition of

about 1 percent calcium montmorillonite fines to a uniform fine sand results

in an order of magnitude decrease in permeability, while over 10 percent

kaolinite fines would be required for a similar reduction in permeability

(Fenn 1966).

j. Summary of Factors Influencing Permeability. The significant

influence that various factors exert on the permeability emphasizes the

importance of duplicating field conditions when determining permeability in

the laboratory.

2-5. Indirect Methods for Determining Permeability.

a. Hazen's Equation. For uniform loose clean sands, classified SP in

the Unified Soil Classification System (U. S. Army Engineer Waterways Experiment Station 1960), the permeability may be estimated from the previously

given Hazen's equation (Taylor 1948)

(2-22)

where k is in cm per second and D10 is in cm.

2-20
2-21

0 

i= 

<( 

MEDIUM 

2.0 

0 

0 

> 

10 10 10 7 10 6 10 5 10 1 10 3 10 

COEFFICIENT OF PERMEABILITY, em/sec 

SOIL IDENTIFICATION CODE 

1. COMPACTED CALICHE 10. OTTAWA SAND 19. LEAN CLAY 

2. COMPACTED CALICHE 11. SAND-GASPEE POINT 20. SAND-UNION FALLS 

3. SILTY SAND 12. SAND-FRANKLIN FALLS 21. SILT -NORTH CAROLINA 

4. SANDY CLAY 13. SAND-SCITUATE 22. SAND FROM DIKE 

5. BEACH SAND 14. SAND-PLUM ISLAND 23. SODIUM-BOSTON BLUE CLAY 

6. COMPACTED BOSTON BLUE CLAY 15. SAND-FORT PECK 24. CALCIUM KAOLINITE 

7. VICKSBURG BUCKSHOT CLAY 16. SILT -BOSTON 25. SODIUM MONTMORILLONITE 

8. SANDY CLAY 17. SILT -BOSTON 26.-30. SAND DAM FIL TEA 

9. SILT -BOSTON 18. LOESS 

Figure 2-11. 

Relationship between void ratio and log of permeability (courtesy of 
EM 1110-2-1901

30 Sep 86

a. Effect of fines on permeability of concrete sand

(from Barber and Sawyer137)

c. Effect of fines on permeability of uniform fine sand

(from Fenn171)

b. Effect of fines on permeability of sand-gravel mixture

(from Barber and Sawyer137)

Figure 2-12. Influence of type and amount of fines on permeability

of concrete sand, sand-gravel mixture, and uniform fine sand

(prepared by WES)

2-22
EM 1110-2-1901

30 Sep 86

b. Masch and Denny Method. For uniform or nonuniform dense clean sands,

classified SP or SW in the Unified Soil Classification System (U. S. Army

Engineer Waterways Experiment Station 1960), the permeability may be estimated

from an empirical method developed by Masch and Denny 1966, and Denny 1965.

The gradation curve is plotted in Krumbein 4 units (Krumbein and Pettijohn

1938) (using the chart in figure 2-13) as shown in figure 2-14 where

(2-23)

where

= phi scale units used to describe grain size distribution

d = grain size diameter in mm

The inclusive standard deviation is used as a measure of the spread of the

gradation curve where (Masch and Denny 1966)

where

= inclusive standard deviation

d1 6 = grain size in units at which 16 percent is finer

d8 4 = grain size in units at which 84 percent is finer

d5 = grain size in units at which 5 percent is finer

d9 5 = grain size in units at which 95 percent is finer

(2-24)

2-23
2-24

10 I I I I I I I I I I I I I I I I I 

8 

6 

4 

2 

0 

-2 

-4 

0.01 

zd 

1 I I I I I I I I I I I I I I I I 

0.1 

GRAIN SIZE, d, mm 

Figure 2-13. Conversion chart for and grain size in mm, for the range 0.01 

(prepared by WES) 
EM 1110-2-1901

30 Sep 86

a. Grain size distribution

b. Coefficient of permeability

versus median grain size

Figure 2-14. Masch and Denny relationship for permeability

as a function of median grain size and inclusive standard

deviation (courtesy of Prentice-Hall175)

2-25
EM 1110-2-1901

30 Sep 86

The median grain size, d50 in units, is determined from the gradation

curve as shown in figure 2-14a. Then knowing and d50 , the coefficient

of permeability in cm per minute can be obtained from figure 2-14b (Freeze and

Cherry 1979).

c. Kozeny-Carman Equation. For uniform loose to dense clean sands

classified SP in the Unified Soil Classification System (U. S. Army Engineer

Waterways Experiment Station 1960), the permeability may be estimated using

the Kozeny-Carman equation (Loudon 1952 and Perloff and Baron 1976)

(2-25)

where

k = coefficient of permeability

= unit weight of fluid

e = void ratio

Cs = shape factor corresponding to a particular flow channel

To = tortuosity factor related to the degree of sinuous flow

sS = specific surface (surface area of solids/volume of solids)

μ = coefficient of viscosity of fluid

For sands and silt-sized (finer than 0.074 mm and coarser than 0.005 mm)

particles CsTo

2

 = 5 is a good approximation (Perloff and Baron 1976). The

specific surface may be obtained from (Loudon 1952)

(2-26)

where

s s = specific surface

A = angularity factor

X1 = percentage of total soil sample between adjacent sieves expressed

as a decimal

sl = specific surface of spheres uniformly distributed in size between

the mesh sizes of adjacent sieves

2-26
EM 1110-2-1901

30 Sep 86

The angularity factor, A , which varies from 1.0 for glass spheres to 1.8 for

crushed glass, may be determined by microscopic examination of the soil or

estimated from table 2-4 (Loudon 1952). The specific surface of spheres,

Si , between the mesh sizes dx and dy is (Loudon 1952)

(2-27)

Specific surfaces of spheres lying between selected U. S. standard sieves is

given in table 2-5.

d. Correlation of In Situ Horizontal Permeability and Hazen's Effective

Grain Size. For natural fine to medium, relatively uniform sands, classified

SP or SW in the Unified Soil Classification System (U. S. Army Engineer

Waterways Experiment Station 1960), in the middle and lower Mississippi River

Valley, the in situ horizontal permeability may be estimated from the Hazen's

effective size as shown in figure 2-15 (U. S. Army Engineer Waterways Experiment Station 1956a). The relationship given in figure 2-15 should not be used

outside the geographic area for which it was developed. A similar relationship

between transmissivity and median grain size of sands is available for the

Arkansas River Valley (Bedinger 1961).

Table 2-4. Angularity Factor for Soil Grains (a)

Type of Material Description Angularity Factor

Glass sphere Well rounded 1.0

Natural sand

Crushed rock

Rounded

Subrounded

Subangular

Angular

Quartzite

1.1

1.2

1.3

1.4

1.5

Crushed rock Basalt 1.6

Crushed glass Pyrex 1.8

(a) Courtesy of the Institution of Civil Engineering210

.

2-27
EM 1110-2-1901

30 Sep 86

Table 2-5. Specific Surface of Spheres Lying Between

Selected U. S. Standard Sieve Sizes (a)

U. S. Standard Sieve Specific Surface (b)

Numbers 1/cm

4 to 6 382

6 to 8 538

8 to 10 696

10 to 16 985

16 to 20 1524

20 to 30 2178

30 to 40 3080

40 to 50 4318

50 to 70 6089

70 to 100 8574

100 to 140 12199

140 to 200 17400

(a) Prepared by WES.

(b)

e. Computation of Permeability from Consolidation Test. The coefficient of permeability of normally consolidated clays and silts can be computed

from the consolidation test using the relationship (Lambe 1951 and Olson and

Daniel 1979)

(2-28)

where

cV = coefficient of consolidation

av = coefficient of compressibility

eo = initial void ratio

2-6. Laboratory Methods for Determining Permeability.

a. General. Laboratory tests described in EM 1110-2-1906 can be used

to determine the coefficient of permeability of a soil, Unless otherwise

required, the coefficient of permeability shall be determined using deaired

distilled water and completely saturated soil specimens. The apparatus used

2-28
EM 1110-2-1901

30 Sep 86

Figure 2-15. Relationship between in situ horizontal

permeability and effective size (prepared by WES

120

)

for permeability testing may vary depending upon whether the sample is finegrained or coarse-grained, undisturbed, remolded, or compacted, and saturated

or unsaturated. The permeability of remolded coarse-grained soils is determined in permeameter cylinders, while the permeability of undisturbed coarsegrained soils in a vertical direction can be determined using the sampling

tube as a permeameter. Samples which have become segregated or contaminated

with drilling mud during sampling operations will not give reliable results.

The permeability of remolded coarse-grained soils is generally used to

approximate the permeability of undisturbed coarse-grained soils in a horizontal direction. Usually the laboratory permeability of remolded coarsegrained soils is considerably less than the horizontal permeability of the

coarse-grained soil in the field, so the approximation may not be conservative. Pressure cylinders and consolidometers are used for fine-grained soils

2-29
EM 1110-2-1901

30 Sep 86

in the remolded or undisturbed state. Fine-grained soils can be tested with

the specimen oriented to obtain the permeability in either the vertical or

horizontal direction.

b. Possible Errors. There are several possible errors in determining

permeability in the laboratory (FM 1110-2-1906; Olson and Daniel 1979;

and Mitchell, Guzikowski, and Villet 1978).

(1) Use of samples that are not representative of actual field conditions. This can be minimized by thorough field investigation, attention to

details (take undisturbed samples from test fills for determination of permeability of embankment materials, sampling along faults, fissures, clay seams,

and sand partings for determination of permeability of the dam foundation),

and by the use of large samples.

(2) Orientation of the in situ stratum to the direction of seepage flow

is seldom duplicated in the laboratory. This can be overcome by obtaining the

permeability of the soil (embankment material and/or foundation) in both the

vertical and horizontal direction.

(3) Incorrect hydraulic gradient used in the laboratory test. The

hydraulic gradient used in the laboratory should cover the range of expected

hydraulic gradient in situ. Where possible the hydraulic gradient should be

selected so that the flow is laminar (straight line relationship between discharge versus hydraulic gradient) and Darcy's law will be applicable. It is

usually not practical to achieve laminar flow for coarser soils, and the

laboratory test should be run at the hydraulic gradient anticipated in the

field.

(4) Air dissolved in the water. As water enters the specimen, small

quantities of air dissolved in the water will tend to collect as fine bubbles

at the soil-water interface and reduce the permeability with increasing time.

Permeability tests on saturated specimens should show no significant decrease

in permeability with time if properly deaired distilled water is used. However, if such a decrease in permeability occurs, then a prefilter, consisting

of a layer of the same material as the test specimen, should be used between

the deaired distilled water reservoir and the test specimen to remove the air

remaining in solution.

(5) Leakage along the sides of the permeameter can result in an

increased permeability. One major advantage of the triaxial compression

chamber for permeability tests is that the specimen is confined by a flexible

membrane which is pressed tightly against the specimen by the chamber pressure

thus reducing the possibility for leakage along the sides.

2-7. Origin, Occurrence, and Movement of Ground Water.

a. Hydrologic Cycle. Precipitation, runoff, storage, and evaporation

of the earth's water follow an unending sequence called the hydraulic cycle,

as shown in figure 2-16. Radiation from the sun evaporates water from the

oceans into the atmosphere. The moisture is condensed and rises to form cloud

formations. From these clouds, the earth receives precipitation of rain,

2-30
EM 1110-2-1901

30 Sep 86

Figure 2-16. Schematic diagram of the hydrologic cycle

(courtesy of Johnson Division, Universal Oil Products 189 )

snow, sleet, or hail which runs into lakes and streams or seeps into the soil

and thence into the underlying rock formations. The percolating water moves

through the saturated subsurface materials and may reappear at the surface, at

a lower elevation than the level where it entered the ground, in the form of

springs and seeps which maintain the flow of streams in dry periods (TM 5-545;

Bureau of Reclamation 1977; and Johnson Division, Universal Oil Products

1972).

b. Water Table. The surface below which the soil or rock is saturated

is the water table, as shown in figure 2-17. The water table is not a level

surface but varies in shape and slope depending upon the variations in permeability and areas of recharge and discharge. In general, the water table

reflects the surface topography but with less relief. Ground water is said to

be perched if it is separated from the main water table by unsaturated materials, as shown in figure 2-17. An aquifer is a saturated permeable geologic

unit that can transmit significant quantities of water under ordinary hydraulic gradients. An unconfined aquifer is one that does not have a confining

layer overlying it as shown in figure 2-17. The water table, or upper surface

of the saturated ground water is in direct contact with the atmosphere through

the open pores of the overlying material and movement of the ground water is in

direct response to gravity. The aquifer may be a layer of gravel or sand,

permeable sedimentary rocks such as sandstones or limestones, a rubbly zone

between lava flows, or even a large body of massive rock, such as fractured

2-31
2-32

level II 

II II II 

Perforated 

Well cosin9 

See text for explanations 

and definitions. 

Figure 2-17. 

II 

II 

II 

I I 

1'1 

II 

II 

II 

II 

II 

Aquiclude 

---

__ _cPiezometric sur foce 

---

Unconfined oquifer 

.. 

• 

c 

0 

;;; 

. 

Groundwater relationsh1ps (courtesy of Soil Conservation Service 
EM 1110-2-1901

30 Sep 86

granite, which has sizable openings. An aquiclude is a saturated geologic

unit that is incapable of transmitting significant quantities of water under

ordinary hydraulic gradients as shown in figure 2-17. A confined or artesian

aquifer has an overlying confining layer of lower permeability than the aquifer and has only an indirect or distant connection with the atmosphere as.

shown in figure 2-17. The water in the artesian aquifer is under pressure and

if the aquifer is penetrated by a tightly cased well or a piezometer, the

water will rise above the bottom of the confining layer to an elevation at

which it is in balance with atmospheric pressure. If this elevation is

greater than that of the land surface at the well, artesian water will flow

from the well as shown in figure 2-17. The imaginary surface, conforming to

the elevations to which water will rise in wells penetrating an artesian

aquifer, is the piezometric surface as shown in figure 2-17 (Soil Conservation

Service 1978, TM 5-545, Bureau of Reclamation 1977, Freeze and Cherry 1979,

and Anonymous 1980).

2-8. Field Methods for Determining Permeability.

a. General. In sands it is difficult to obtain undisturbed soil

samples for laboratory testing and the structure (void ratio, stratification,

etc.) has an important influence on-permeability. Therefore, field tests for

determining permeability are necessary. Because sampling operations do not

necessarily indicate the relative perviousness of foundations containing large

amounts of gravelly materials, field pumping tests are required to determine

the foundation permeability for dams where positive measures are not proposed

to completely cut off underseepage in the gravelly formations.

b. Test Pits and Bore Hole Tests.. In sands and gravels above the

ground-water level, field tests are normally carried out by measuring the downward seepage from test pits or shallow boreholes (Cedergren 1977). Below the

ground-water table information about the order of magnitude and variability of

the coefficient of permeability may be obtained by conducting falling head

permeability tests in the exploratory boring as drilling proceeds. The hole

is cased from the ground surface to the top of the zone to be tested and

extends without support for a suitable depth below the casing. If the pervious stratum is not too thick, the uncased hole is extended throughout the

full thickness, otherwise the uncased hole penetrates only a part of the

pervious stratum. Water is added to raise the water level in the casing and

then the water level descends toward its equilibrium position. The elevation

of the water level is measured as a function of time and the coefficient of

permeability is calculated (Terzaghi and Peck 1967).

(2-29)

where

k = coefficient of permeability

2-33
EM 1110-2-1901

30 Sep 86

A = inside cross-sectional area of casing

drop in water level in casing during time interval At

time interval

C = dimensionless quantity depending on shape of cylindrical hole and

depth of penetration into pervious zone (see figure 2-18)

= mean radius of hole below casing

= mean distance during time interval At from water level in casing

to equilibrium water level in pervious zone

The falling head field permeability test often gives an observed permeability

that is too low because silt particles which are suspended in the water may

form a filter skin over the walls and bottom of the hole in the pervious material. The results of such tests are little more than an indication of the

order of magnitude of the in situ permeability. More reliable data are

obtained from field pumping tests.

c. Field Pumping Tests. The most reliable method for determining in

situ permeability is a field pumping test on a test well which fully penetrates the aquifer. The test procedures for equilibrium (steady-state flow)

and nonequilibrium (transient flow) are given in Appendix III to TM 5-818-5

and Civil Works Engineer Letter 63-16 (U. S. Army Corps of Engineers 1963).

The ratio of the horizontal to vertical permeability can be determined from

specially conducted field pumping tests (Mansur and Dietrich 1965).

2-9. Chemical Composition of Ground Water and River (or Reservoir) Water.

a. Ground Water. The chemical composition of the ground water is important because some ground waters are highly corrosive to metal screens, pipes,

and pumps, or may contain dissolved minerals or carbonates which form incrustations in wells or filters and, with time, cause clogging and reduced efficiency of the dewatering or drainage system. Indications of corrosive and

incrusting waters are given in table 2-6 (TM 5-818-5; and Johnson Division,

Universal Oil Products 1972). General information concerning ground-water

properties is available in an Atlas (Pettyjohn et al. 1979). Sampling, sample

preservation, and chemical analysis of ground water is covered in handbooks

(Moser and Huibregtse 1976, and Environmental Protection Agency 1976).

b. River (or Reservoir) Water. The total amount of cations (calcium,

magnesium, potassium, and sodium) in the river water (for dams not yet constructed) and in the reservoir water (for existing dams) significantly influences the erosion through a possible crack in the core of the dam (Perry 1975).

Usually, as the total amount of cations in the eroding water decreases, the

erodibility of the soil increases. For dams constructed of dispersive clay,

the susceptibility of the dam to piping depends, in part, upon the total amount

of cations in the seepage water (Perry 1979).

2-34
EM 1110-2-1901

30 Sep 86

Figure 2-18. Field permeability test in bore hole

(courtesy of John Wiley and Sons175)

2-35

4000 

2000 

1000 

700 

1..> ~00 

' 

-~ 2~0 

-" ,;:: 

-...: 

"' !00 (3 70 

40 

20 

JO 

7 

(b) 

L .. • For if; <20"-, vse L •L 

~ 

= 

~ 

-

-

~ 

t1--

1--

5 m ~ M ~ ~ ~ ~ ~ 

Ratio~ ro 

(a) 

I IT II I I I II -r If 

-- --

/ 

v 

I/ v 

/ 

I/ 

l/ v 

v v 

v I I I II I I I l11 I I I 

T1 / 

/ 

/ 

/ = 

-

-

-

= 

-

-

-

II ~ 

I 2 ~ 7 /0 20 40 70 /00 200 ~ 700 1000 2000 4000 

Rt~tio ~ ro (c) 
EM 1110-2-1901

30 Sep 86

Table 2-6. Indicators of Corrosive and Incrusting Waters (a)

Indicators of Corrosive Water Indicators of Incrusting Water

1.

2.

A pH less than 7 1. a pH greater than 7

Dissolved oxygen in excess of

2 ppm(b)

3. Hydrogen sulfide (H2S) in excess of 3. Total manganese (Mn) in excess of

1 ppm, detected by a rotten egg 1 ppm in conjunction with a high

odor pH and the presence of oxygen

4. Total dissolved solids in excess of

1000 ppm indicates an ability to

conduct electric current great

enough to cause serious electrolytic corrosion

5. Carbon dioxide (C02) in excess of

50 pm

6. Chlorides (CL) in excess of 500 ppm

2. Total iron (Fe) in. excess of

2 ppm

4. Total carbonate hardness in

excess of 300 ppm

(a) From TM 5-818-51

.

(b) ppm = parts per million.

2-36
EM 1110-2-1901

30 Sep 86

CHAPTER 3

DETERMINATION OF PERMEABILITY OF ROCK

3-1. Permeabilities of Rock Masses. Permeability of rock, as with soil, is a

measure of the ease-with which fluids may travel through a medium under the

influence of a driving force. The term "permeability," however, has several

definitions for describing the flow of water in rock masses.

a. Coefficient of Permeability. The engineer's coefficient, or Darcy's

coefficient, is normally referred to as simply the "coefficient of permeability." It is defined as the discharge velocity through a unit area under a

unit hydraulic gradient and is dependent upon the properties of the medium, as

well as the viscosity and density of the fluid (Section 2-3.a.).

b. Intrinsic Permeability. The physicist's coefficient, or the intrinsic permeability, is occasionally used in the determination of the hydraulic

conductivity of a rock mass. It is defined as the volume of a fluid of unit

viscosity passing through a unit cross section of a medium in unit time under

the action of a unit pressure gradient (Section 2-3.b.). The intrinsic permeability thus varies with the porosity of the medium and is independent of both

the viscosity and the density of the fluid.

c. Equivalent Permeability. The complex system of interconnected void

space in a rock mass may be described in terms of an equivalent porous continuum, and the flow assumed to occur uniformly throughout the mass rather

than within individual passageways. Under these assumptions the term equivalent permeability is used to describe the permeability of a rock mass.

\

d. Parallel Plate Permeability. The permeability of a fissure or a

fissure set is occasionally determined by modeling the rock mass conditions

with parallel plates. The parallel plate permeability can be computed from

the value of the aperture between the plates (Ziegler 1976) and this permeability provides inferences for use in the

computed parallel plate permeabilities has

laboratory tests (Snow 1965).

modeled rock mass. The accuracy of

been verified consistently with

e. Fissure Permeability. Fissure permability is the permeability of

an individual fissure or a set of fissures and, whether measured in the

laboratory or in the field, is determined using the parallel plate permeability

theory. Fissure permeability is determined using an equivalent parallel plate

aperture, rather than the actual fissure aperture. This in effect incorporates roughness into the parallel plate law.

3-2. Flow Characteristics in Rock Masses. The determination of the permeability of a rock mass, whether it be a rock slope, dam foundation, or dam

abutment, can only be accomplished after certain criteria are defined or

specified.

a. Continuum Approximations. From an overall regional point of view,

most rock masses may be treated as continua, for all practical purposes. One

of the primary considerations in selecting the continuum approach,-for evaluating the permeability of a rock mass, is the relative size, frequency, and

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orientation of the inherent discontinuities in the rock mass, compared with

the size of the area of interest or area under study. If the flow characteristics of a rock mass are to be treated as those of continua, the net variation in flow over the study area should be relatively small, and the frequency

and orientation of the discontinuities should be such that they provide an

overall averaging effect on the flow with respect to the area of interest.

b. Discontinuum Approximations. As areas of investigation become

smaller and smaller, i.e. more specific, the inherent discontinuities in rock

masses start to play larger and larger roles in the interpretation of groundwater flow and its path of movement. The permeabilities or relative permeabilities of individual fissures and fissure systems are important for estimating the amount of seepage into various sections of underground excavations

such as powerhouse tunnels or diversions , or through specific strata in a dam

foundation or abutment. Discontinuum approximations of permeability are normally used when the flow in the area of investigation is governed either by a

single fissure or by a fissure system.

(1) Single Fissure Flow. The permeability of single fissures can be

very important in karstic terrains, basalt, or rhyolite flows, or in areas

where tunnels are driven through faulted zones. The flow through a single

fissure, under certain geologic conditions, can be the key to estimating the

seepage through a dam foundation or abutment, or for determining the best

route for a proposed tunnel.

(2) Flow Through Fissure Systems. Fissure systems such as joints,

fractures, and bedding planes can yield, or contribute to, unpredictable flow

paths, seepage patterns, and uplift pressures. The permeability of fissure

systems should be evaluated by a discontinuum method of analysis when the

size, frequency, and orientation of such systems make a continuum approach to

the area under investigation unrealistic.

c. Ground-water Velocity. Flow of water in rock masses is generally

considered to be governed by one of two laws. Under conditions of laminar

flow, Darcy's law, previously presented as equation 2-1 in Chapter 2 is assumed

to govern the flow. For turbulent flow conditions in rock there is a nonlinear

flow velocity versus hydraulic gradient relationship and equations presented by

Forchheimer (1914) and Missbach (1937) are assumed to govern the flow. The

Missbach law is the most convenient to analyze and it takes either of

two forms,

(3-1)

or

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(3-2)
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where

m and = degrees of nonlinearity

k' and B' = turbulent coefficients of permeability

Since the two equations are identical, resolving them indicates that m =

and The use of the above laws, however, is usually restricted

to a homogeneous, isotropic, porous continuum. Since in soil and rock masses

there are complex systems of interconnected void spaces, an equivalent rather

than an absolute permeability should be determined. The coefficient of equivalent permeability from the continuum approach assumes that flow occurs uniformly throughout the mass rather than within individual passageways. Therefore, for equivalent permeability, Darcy's law and Missbach's law are written,

respectively,

(3-3)

and

(3-4)

where

ke = laminar equivalent permeability

turbulent equivalent permeability

The continuum approach, in some cases, is not applicable and therefore, the

discontinuum method of analysis for evaluating an equivalent permeability

should be used. Formulae for the discontinuum analysis for equivalent

permeability are presented later with various other methods of analysis.

3-3. Methods for Determining Rock Mass Permeability. Numerous methods have

been developed for determining or estimating rock mass permeabilities. All of

the available testing, as well as analytical techniques should be considered

and evaluated for each individual study, in order to optimize the advantages

and minimize the disadvantages inherent within each method for determining the

permeability of a rock mass.

a. Laboratory Permeability Tests. Laboratory permeability tests are

used for evaluating the permeability of rock cores or samples, determining the

flow characteristics of rock fissures, and performing parametric studies of

the factors affecting the permeability of rock masses. Laboratory test

methods for permeability provide a convenient research and evaluation tool

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because a variety of parameters may be controlled and varied to yield a broad

spectrum of conditions which may be encountered in a rock mass.

(1) Model Tests. Model tests are conducted by constructing parallel

plate models to simulate given geologic information. The tests generally tend

to be a parametric evaluation, but have been used extensively in evaluating

both theoretical and empirical rock mass permeability formulae. To model fissures as equivalent parallel plate conductors, the flow between parallel

plates must be defined (Snow 1965 and Wilson and Witherspoon 1970). Laminar

flow of an incompressible viscous fluid between smooth, parallel plates can be

expressed as

where

= unit weight of water

= dynamic viscosity of water

d = aperture between smooth parallel plates

The volume flow rate per unit width, q , becomes

(3-5)

(3-6)

Comparison of the flow velocity equation with Darcy's law indicates that the

parallel plate permeability, kp , can be expressed by

(3-7)

where

(2) Individual Fissure Tests. The majority of the laboratory tests

which have been conducted, to date, have been on individual fissures. Tests

on individual fissures are perhaps the most flexible of the laboratory tests

for rock mass permeability. The tests are generally conducted at various flow

rates within the individual fissure and at various normal loads to simulate

the in situ effective stress flow conditions. The data are used to develop

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correlations for predicting the permeability under the anticipated in situ

stress and hydraulic gradient conditions. The permeability measured from

individual fissures provides direct input into discontinuum analyses and may

be applied to continuum analyses under certain conditions. Before fissure

permeability, kj , can be determined, however, the fissure roughness must be

incorporated into the equation for the parallel plate permeability, kp . To

accommodate the roughness, the aperture between smooth, parallel plates, d ,

is replaced with an equivalent parallel plate aperture, e . Thus, the fissure

permeability is expressed by

(3-8)

where Thus, it follows that the flow rate per unit width

becomes

(3-9)

The value of e can be determined from flow experiments by rearranging the

above equation to the form

(3-10)

Values for e are determined from laboratory tests on individual fissures,

and equations for the laminar equivalent permeability have been developed

yielding

(3-11)

where

e

avg

= average of individual values of e for fissures in the set under

consideration

b

avg

= average of the individual spacing between fissures

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Tests of individual fissures can also be analyzed for turbulent flow according

to the Missbach law

(3-12)

where the volume flow rate per unit width can be expressed as

The turbulent coefficient of permeability thus given by

(3-13)

(3-14)

The degree of nonlinearity, m , is determined as the arithmetic slope of

log i versus log q (Ziegler 1976). For turbulent flow analysis the

equivalent parallel plate aperture, e , is estimated from analysis of the

linear portion of the q versus i curve given by

(3-15)

(3) Representative Sample Tests. Another laboratory approach to

measuring permeability is to test a representative sample from a rock mass.

The obvious difficulty with such tests, however, is the problem of obtaining a

representative specimen of reasonable dimensions. The tests may be conducted

as standard laboratory permeability tests, but on a larger scale. In addition

to the standard permeability tests, small-scale pressure injection tests may be

conducted on such specimens, but only a limited amount of success should be

expected.

(4) Evaluation of Methods of Analysis. Model tests, as well as the

testing of representative samples, have only limited application and the

results are frequently subject to much speculation. Measured fissure permeability and computed equivalent permeability can be directly applied to discontinuum and continuum analyses, respectively. In general, laboratory tests

are normally representative of only a very small portion of the rock mass under

consideration. In addition, the results of such tests can be altered

significantly by either the control or the interpretation of the parameters

involved in the test. Laboratory tests, therefore, should be used as a supplement to, rather than in lieu of, field tests.

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b. Interpretation from Geologic Properties. Theoretical and empirical

formulae have been developed which relate permeability to geologic properties.

The parameters generally required for interpretation, or computation, are the

average fissure aperture, the average surface roughness of the fissures, and

the average fissure spacing or number of fissures per given length. The

governing assumption for any interpretation by this method is that the rock

mass permeability is controlled by fissures and that the fissures may be

modeled as equivalent parallel plate conductors. Extensive borehole logging

or observation and mapping of exposed surfaces is required for determining the

parameters to be used in the analysis.

(1) Analytical Procedures. If no laboratory tests are performed to

determine an equivalent parallel plate aperture, an equivalent permeability can

be estimated solely from field data. The requirements are core samples for

determining surface roughness of fissures and borehole logging to determine the

fissure apertures and spacing. To evaluate the surface roughness of fissures,

Louis (1969) defined a surface roughness index, S , as

(3-16)

where

y = mean height of the asperities on the fissure walls

a = mean fissure aperture

For S < 0.033 equations for laminar equivalent permeability have been developed which yield

(3-17)

where a

avg

= average of the individual values of a . For S > 0.033 equations for the laminar equivalent permeability have been developed which yield

(3-18)

where S

avg

= average of the individual values of S . The above equations

generated by Louis (1969) are empirical and are the result of numerous pipe

flow experiments and separate tests of fissures with different roughness,

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modeled as openings between parallel slabs of concrete. In addition to laminar

flow formulae, equations may be developed for turbulent flow for both the

hydraulically smooth and the completely rough flow regimes.

(2) Evaluation of Method of Analysis. Comparisons of permeability

interpreted from geologic properties with permeability measured by other

methods have indicated the potential for large differences between the computed and the actual permeability. Interpretations of permeability from fissure properties are made difficult by obvious problems in measuring fissure

apertures and roughness.' Natural fissures can have complex surficial geometries and can only be observed in boreholes or exposed surfaces, which may be

disturbed during excavation. Potentially large discrepancies are possible, due

to the possibility of many fissures near the borehole being either exaggerated,

constricted, or discontinuous, due to the disturbance during drilling. While

interpretation of permeability from geologic properties is theoretically possible, the results should be used with caution.

c. Field Measurements. By far the most accurate and most reliable

technique for determining the permeability of a rock mass is that of field

testing. The use of field tests results in larger volumes of the rock mass

being tested and the tests are performed under in situ conditions. Field

tests have generally been limited to ground-water velocity measurements, pumping tests, and injection tests.

(1) Ground-water Velocity Measurements. The equivalent permeability can

be computed for a rock mass by measuring the ground-water velocity and the

hydraulic gradient when certain criteria are met. It must be assumed that

steady-state horizontal flow intersects the well and flow is governed by

Darcy's law. There are several techniques available for measuring ground-water

velocity downhole as discussed below.

(a) Temperature Probes. The velocity of ground water moving through a

borehole may be determined with the use of temperature probes or sensors. Such

devices consist of a small heater strip or coil mounted beneath a thermistor.

The amount of heat dissipated is a function of the ground-water velocity, and

properly calibrated, the devices can sense very low velocities (below

1 ft/min). The directional components of flow may be obtained by rotation of

the device or by the construction of orthogonal flow channels within the device

itself.

(b) Flowmeters. When conditions of high ground-water flow rates are

encountered, small horizontally mounted commercial flowmeters may be placed

downhole for measuring the velocity. The direction of flow may be determined

by varying the orientation of the flowmeter.

(c) Tracer Tests. Tracer tests involve the injection of an inert solution, or tracer, into an existing flow field via a borehole or well. Tracer

tests are often desirable because they are passive-type tests and do not place

unnatural stress conditions on the flow system. The dilution rate of the

tracer at the injection well or its time of travel to another well can be used

to calculate the ground-water velocity and ultimately the permeability. Detection of the tracer, or concentration measurements, can be made by either

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manual or probe sampling. Generally, the probe method of sampling is desirable

to avoid any disturbance to the flow system due to sample extraction. The

"travel time" tracer tests normally involve large portions of the rock mass,

and thus have the advantage of averaging the effects of exceptionally high- or

low-permeability zones within the mass. The dilution method of testing is

particularly applicable to determining permeability profiles within a single

borehole by injection of the tracer into borehole sections isolated by packers.

Commonly used tracers are radioisotopes, salt solution, and fluorescent dyes.

(d) Methods of Analysis. Downhole ground-water velocity measurement

devices such as a temperature probe or flowmeters measure the Darcy velocity or

discharge according to his original equation, expressed as

(3-19)

or

(3-20)

With the hydraulic gradient determined from observation wells in the area, the

permeability can be computed directly. For tracer tests the seepage velocity

is determined according to the equation

where

dW = distance between injection well and observation well

tr = tracer travel time between wells

Using the relationship

(3-21)

(3-22)

(3-23)

(3-24)

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In analyzing a tracer dilution test, the flow velocity, v , is related to the

rate at which the tracer concentration diminishes within the test section of

the injection well. For an assumed homogeneous isotropic porous medium, the

velocity is determined from the following equation given by Lewis, Kriz, and

Burgy (1966).

(3-25)

where

wd

= well diameter

Cr = ratio of the final to the initial tracer concentration

td = dilution time period

Analysis of dilution tests in fractured and fissured rock masses is made by

applying the parallel plate analogy.

(2) Pumping Tests. Pumping tests have become an established means of

determining the permeability of hydraulic characteristics of water bearing

materials. In a pumping test, water is pumped from a well normally at a

constant rate over a certain time period, and the drawdown of the water table

or piezometric head is measured in the well and in piezometers or observation

wells in the vicinity. Since pumping tests, as with tracer tests, involve

large volumes of the rock mass, they have the advantage of averaging the

effects of the inherent discontinuities, such as joints, fissures, fractures,

etc. Most classical solutions for pump test data are based on the assumptions

that the aquifers are homogeneous and isotropic, and that the flow is governed

by Darcy's law. Applications of such solutions to interpretation of pumping

tests in rock masses have resulted in varying degrees of success. For cases

where the normal solutions have proven to be unsuccessful or inadequate,

mathematical models have been developed which are capable of modeling the flow

regime in various types of rock masses. With pumping tests, the major disadvantage is the period of time required to perform a test. Test durations of

one week or longer are not unusual when attempting to approach steady-state

flow conditions. Additionally, large diameter boreholes or wells are required

since the majority of the conditions encountered require the use of a downhole

pump. The analysis of pumping test results obtained from rock masses is

generally completely analogous to the analyses used in classical soil

mechanics. Since such analyses are well-documented, they will not be presented here.

(3) Injection Tests. Injection tests, which are the reciprocal of

pumping tests, commonly involve the steady-state transmission of a fluid from a

borehole into the surrounding medium. The permeability of a rock mass can be

related to the relationship between the injection pressure and the flow rate.

Equations and techniques have been developed for both the steady-state and the

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unsteady-state conditions and for using either air or water for injection.

Methods of analysis of pressure injection tests are presented in Appendix C.

(a) Water Pressure Tests. Water pressure tests, also known as packer

tests (in Europe they are called Lugeon tests) are normally conducted by

pumping water at a constant pressure into a test section of a borehole and

measuring the flow rate. Borehole test sections are commonly sealed off by

one to four packers, with the use of one or two packers being the most widely

used technique. In comparison with a pumping test, a water pressure test

affects a relatively small volume of the surrounding medium, because frictional

losses in the immediate vicinity of the test section are normally extremely

large. The test, however, is rapid and simple to conduct, and by performing

tests within intervals along the entire length of a borehole, a permeability

profile can be obtained. Additionally, the water pressure test is normally

conducted in NX boreholes, and has the advantage of being conducted above or

below the ground-water table.

(b) Air Pressure Tests. Air pressure tests are similar to water pressure tests except that air rather than water is used for the testing fluid.

The air pressure test was developed for testing above the ground-water table

and has predominantly been used for testing areas of high permeability such as

those characteristic of rubblelike, fallback material adjacent to explosively

excavated craters in rock. In such areas, water pressure tests have been

inadequate due to an inability to provide water at a flow rate high enough to

pressurize the surrounding media. Air pressure tests have an unlimited supply

of testing fluid, as well as the advantage of a wide variety of high capacity

air compressors. The disadvantage of such tests is that permeability equations

must be modified for application to a compressible fluid and a conversion from

the air permeability to a water permeability must be made to obtain usable

results.

(c) Pressure Holding Tests. Pressure holding or pressure drop tests are

usually conducted in conjunction with water pressure tests. The test is

analogous to the falling head test used in soil mechanics; however, in rock

the test section is normally pressurized to a value above that of the static

head of water between the test zone and the ground surface. The pressures are

normally measured in the test section with a transducer, and pressures versus

time are recorded. The pressure holding test offers the advantage of being

quick and simple to perform, as well as requiring significantly less water

than that used in conventional constant pressure tests.

3-4. Applications of Rock Mass Permeability.

a. Assessment of Ground-water Movements. The permeability of a dam's

foundation or abutments is one of the controlling factors in the movement of

ground water; therefore,. a valid assessment is imperative. The rock mass

permeability of the dam foundation or abutment has numerous applications, each

having potentially significant impact on the design or safety of the

structure.

(1) Seepage Patterns. Seepage patterns which are expected to develop

after impoundment of a reservoir should be evaluated during the design phase of

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a dam. Seepage patterns which do actually develop after a reservoir is in

operation provide valuable data for an evaluation of the as-built performance

of any cutoff or relief measures, sources and exits of seepage, and input for

planning required remedial measures, such as additional cutoffs, drains, etc.

In rock masses, generally, the overall trend of the seepage patterns can be

determined by the continuum approach; however, in some cases, a detailed

analysis of a specific seepage problem requires the use of a discontinuum

approach.

(2) Flow Rates. Given the permeability and gradient, the flow rate

across a given area can be computed. With the effective porosity, the rate of

advance of a seepage front can be determined. Ground-water flow rates are

required for determining construction dewatering requirements for both surface

and subsurface excavations, as well as the seepage losses through dam foundations and abutments.

b. Foundation and Abutment Drainage Requirements. The permeability of

a dam's foundation and abutments is the major factor involved in evaluating

drainage requirements. Accurate and reliable rock mass permeability measurements are required in the design phase for determining the necessity for, and

extent of, cutoff, vertical drains, drainage blankets, relief wells, etc.

Postconstruction problems with leakage, excessive uplift pressures, etc., also

require an in-depth evaluation of the flow of the water in a foundation or

abutment. Evaluations of drainage or relief requirements are generally

directed toward specific areas and, in most cases, while a continuum approach

can give satisfactory approximations, the discontinuum analysis is required

for describing the flow characteristics in details.

c. Grouting Requirements and Effectiveness. Consistent with determining

the drainage requirements for a structure, the permeability is also useful for

estimating the grouting requirements. In the design phase of a dam the

requirements for cutoff or grouting, and drainage or relief, compliment each

other and are balanced to obtain a desired seepage pattern and uplift pressure

distribution beneath or within the structure. In foundations, and particularly

in abutments, permeability measurements can indicate possible solution channels, faults, fissures, or other highly permeable zones which require grouting. If permeability tests are conducted at a given location, both before and

after a grouting operation, an evaluation of the grouting effectiveness can be

made. Such tests should be conducted as a matter of routine since they will

either establish a confidence level or indicate the need for additional

grouting.

d. General Considerations. The application of rock mass permeability

to seepage control methods and evaluations has become increasingly useful as

more complex methods of analysis evolve.

(1) Index Tests. The determination of rock mass permeability for dam

foundations and abutments has historically been used more as an index test

than as an absolute test. As the state of the art advances this trend is

gradually changing. While index tests are a valuable tool to the experienced

foundation engineer, more complex methods of analysis are becoming available

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which allow a complete evaluation of the mechanisms involved as water flows

through a fractured or fissured rock mass.

(2) Continuum Analyses. The accuracy of continuum approximations of

permeability is dependent upon the geology and the size of the area under

consideration. In general, continuum analyses provide average permeabilities

or regional permeabilities in which the assumptions of isotropy and homogeneity can be used in a gross sense. From a practical point of view the continuum

approach has been and continues to be a useful tool for evaluating rock mass

permeability.

(3) Discontinuum Analyses. Recently the discontinuum approach to

determining permeability has become more and more promising. As techniques for

determining individual fissure permeabilities advance, the availability of

better modeling techniques increases, and understanding of the influences of

orientation, spacing, apertures, and surficial geometries of fissures and fissure sets increase, the discontinuum approach to determining rock mass permeability becomes more reliable.

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CHAPTER 4

SEEPAGE PRINCIPLES

4-1. General Considerations. Seepage as used in this manual is defined as

the flow of water through homogeneous saturated soil under steady-state conditions. Additionally, the soil particles, soil structure, and water are

assumed incompressible and flow obeys Darcy's law. Thus transient conditions

such as a wetting front or other movement of water in unsaturated soil, consolidation, and subsidence are not considered for analysis. Principles which

characterize movement of energy through conducting media also apply to the

movement of water through soils. Seepage has been modeled for study by using

flow of electricity and heat. Both conditions are governed by Laplace's equation in homogeneous media. As explained in Chapter 2, water moves from a

higher energy state to a lower energy state, and in seepage the difference in

energy states is the amount of energy required to move the water through the

soil, i.e., to overcome the soil's resistance to the flow of water. Chapter 4

will consider factors controlling seepage, equations describing seepage,

methods of determining pressure distribution and pressures at particular points

in the soil, and seepage quantities. For example, in figure 4-1(a): What is

the uplift pressure at point 5? How much water will exit at point 8? How

fast? Will the sand at point 8 be eroded? If the sheet pile at point 6 is

removed, how will it affect pressure distribution beneath the dam?

4-2. Boundary Conditions.

a. Basis. The saturated soil which is considered for analysis must be

defined by boundaries, permeability of the soil, and heads imposed upon the

water. This section considers the types of boundaries which may define a

particular porous soil mass considered for analysis. The nature and location

of these boundaries are determined by a soils exploration program, assumptions

based on engineering judgment and conditions imposed by the proposed design.

Normally, simplifying assumptions are required in order to establish boundaries

which will make analysis feasible. Generally, seepage analysis problems

associated with dams will involve four possible types of boundaries (Harr

1962). Examples of the four general types of boundary conditions are shown in

figure 4-1.

b. Impervious Boundaries. The interface between the saturated, pervious soil mass and adjacent materials such as a very low permeability soil or

concrete is approximated as an impervious boundary. It is assumed that no flow

takes place across this interface, thus flow in the pervious soil next to the

impervious boundary is parallel to that boundary. In figure 4-1, lines AB and

1-8 are impervious boundaries.

c. Entrances and Exits. The lines defining the area where water enters

or leaves the pervious soil mass are known as entrances or exits, respectively. Along these lines (O-l and 8-G in figure 4-1(a) and AD and BE in

figure 4-1(b)) are lines of equal potential; that is, the piezometric level is

the same all along the line regardless of its orientation or shape. Flow is

perpendicular to an entrance or exit. Entrances and exits are also called

reservoir boundaries (Harr 1962).

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Figure 4-1. Examples of boundary conditions (courtesy of

McGraw-Hill Book Company 180 )

d. Surface of Seepage. The saturated pervious soil mass may have a

boundary exposed to the atmosphere and allow water to escape along this

boundary, line GE, figure 4-1(b). Pressure along this surface is atmospheric.

The surface of seepage may also be called a seepage face.

e. Line of Seepage. Known also as the free surface, this boundary is

located within the pervious soil where water is at atmospheric pressure,

line DG, figure 4-1(b). Because of capillary forces, the saturated zone of

pervious soil extends slightly above the line of seepage, but this capillary

zone rarely has significant influence on seepage analysis. Whereas the first

two boundaries are normally defined by the geometric boundaries of the saturated porous soil mass, the line of seepage is not known until the flow distribution within the pervious soil is known. Again, as for an impervious

boundary, the assumption is made that no flow takes place across the line of

seepage, thus flow in the pervious soil next to this boundary is parallel to

the boundary.

4-3. Confined and Unconfined Flow Problems. Two general cases of seepage are

considered in this manual: confined and unconfined flow. Confined flow

exists in a saturated pervious soil mass which does not have a line of seepage

boundary. Figure 4-1(a) is an example of confined flow. Unconfined flow,

figure 4-1(b), exists when the pervious soil mass has a line of seepage. Thus

confined flow has all boundaries defined while for unconfined flow the surface

of seepage and line of seepage must be defined in the analysis.

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4-4. Laplace's Equation.

a. Seepage Analysis. In order to do a seepage analysis, a general

model describing the phenomena of seepage must be available. Supplied with

specific boundary conditions and soil properties, this model can be used to

determine head and flow distribution and seepage quantities. The Laplace

equation is the mathematical basis for several models or methods used in

seepage analysis.

b. Basis of Laplace's Equation. Figure 4-2 shows a general seepage

condition from which an element is taken. Development of Laplace's equation

depends on six assumptions:

(1) Heads h 1and h2

are constant and thus flow is steady state.

(2) Water is incompressible.

(3) Volume of voids does not change--soil is incompressible.

(4) Flow is laminar--Darcy's law applies.

(5) The element has a dimension, dy , into the plane of the figure

which gives an element volume but no flow takes place perpendicular to the

plane of the figure, i.e., the flow is two-dimensional.

(6) The saturated pervious soil stratum is homogeneous. From

figure 4-2(b) let:

v ,v

x z

= components of discharge velocity in x and z directions,

respectively

hydraulic gradient in the x direction

hydraulic gradient in the z direction

(The minus sign indicates that gradient is in a direction opposite increasing

piezometric head.) Assumptions 1, 2, and 3 assure continuity of flow which

means that water entering the element per unit of time, q e (where qe = vx

dz dy + vz dx dy) equals water leaving the element per unit of time,

(where Setting

equal to gives:

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(4-1)

Using Darcy's law, v = ki and assuming the same permeability in the x and

z directions:

kh is called a potential or velocity potential and is normally given the

symbol Thus

and

Substituting into equation 4-1 gives

(4-2)

which is a form of the Laplace equation for laminar, two-dimensional flow in

homogeneous, isotropic, porous media. The development here follows Terzaghi

1943. Rigorous developments can be found in Bear 1972, Cedergren 1977, and

Harr 1962.

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Figure 4-2. Flow of water through saturated pervious soil

beneath a hydraulic structure (courtesy of John Wiley and

Sons274)

4-5. Methods for Solution of Laplace's Equation. Solutions to steady-state,

laminar flow, seepage problems must solve Laplace's equation. Several methods

have been developed to solve exactly or approximately Laplace's equation for

various cases of seepage, figure 4-3 (Radhakrishnan 1978). One of the most

widely used methods, the flow net, can be adapted to many of the underseepage

and through-seepage problems found in dams and other projects involving

hydraulic structures. This method will be covered in detail in Section 4.6.

a. Models. Models which scale or simulate the flow of water in porous

media can provide a good feel for what is occurring during seepage and allow a

physical feel for the reaction of the flow system to changes in head, design

geometry, and other assumptions. Appendix B contains examples of the various

model types.

(1) As previously mentioned, processes which involve movement of energy

due to differences in energy potential operate by the same principles as

4-5
4-6

I 

FLOW NETS 

a. 

b. 

c. 

I SEEPAGE ANALYSIS I 

J J 

MODELS ANALYTICAL METHODS NUME

COMPUT

ELECTRICAL ANALOGY a. MAPPING OR a. 

(1) WET--AQUEOUS TRANSFORMATION 

SOLUTION OR b. SEMI EMPIRICAL GEL 

2-D OR 3-D -METHOD OF b. 

(2) DRY 2-D FRAGMENTS 

SAND c. CLOSED FORM 

2-D OR 3-D 

VISCOUS FLOW 

2-0 

Figure 4-3. 66 Seepage analysis methods (from Radhakrishnan ) 

FINITE 

(RELAX

1,2,3-D

FINITE 

1,2,3-D
EM 1110-2-1901

30 Sep 86

movement of confined ground water. These processes include electricity and

heat flow which have been used as seepage analogies. Electrical analogies have

proven particularly useful in the study of three-dimensional problems and in

problems where geometric complexities do not allow adequate simplifying

assumptions for analytical methods. "Wet" electrical analogies normally use a

conducting aqueous solution or gel to model the volume of the confined, saturated, porous soil. Wet models are well suited to projects where an irregular

structure penetrates a confined aquifer. By probing the gel or solution when

a set potential or voltage is applied across it, electrical potential can be

determined at various points of interest in the model aquifer (McAnear and

Trahan 1972, Banks 1963, 1965). When field conditions can be characterized by

a two-dimensional plan or section, conducting paper models may be used to

inexpensively determine the effect of various configurations on the flow and

pressures in the aquifer, figure 4-4 (Todd 1980).

(2) Sand models which may use prototype materials can provide information about flow paths and head at particular points in the aquifer. The sand

or porous material may be placed underwater to provide a homogeneous condition, or layers of different sand sizes may be used to study effects of internal boundaries or layers. If the flow is unconfined and the same material is

used for model and prototype, the capillary rise will not be scaled and must

be compensated for in the model. Flow can be traced by dye injection and

heads determined by small piezometers. Disadvantages include effects of

layering when the porous material is placed, difficulty in modeling prototype

permeability and boundary effects. Prickett (1975) provides examples of sand

tank models and discusses applications, advantages, and disadvantages.

(3) Viscous flow models have been used to study transient flow (e.g.,

sudden drawdown) and effects of drains. This method depends on the flow of a

viscous fluid such as oil or glycerin between two parallel plates and is normally used to study two-dimensional flow. As with sand models, dye can be

used to trace flow lines.' Construction is normally complicated and operation

requires care since temperature and capillary forces affect the flow. Flow

must be laminar, which can be difficult to achieve at the boundaries or at

sharp changes in boundary geometry.

b. Analytical Methods.

(1) Harr (1962) explains the use of transformations and mapping to

transfer the geometry of a seepage problem from one complex plane to another.

In this manner, the geometry of a problem may be taken from a plane where the

solution is unknown to a plane where the solution is known. While this method

has been used to obtain solutions to general problems it is not frequently

used for solutions to site-specific seepage problems since it requires the use

of complex variable theory and proper choice of transformation functions.

(2) Pavlovsky (1936, 1956) developed an approximate method which allows

the piecing together of flow net fragments to develop a flow net for the total

seepage problem. This method, termed the Method of Fragments, allows rather

complicated seepage problems to be resolved by breaking them into parts,

analyzing flow patterns for each, and reassembling the parts to provide an

4-7
EM 1110-2-1901

30 Sep 86

Figure 4-4. Use of two-dimensional conducting paper to find flow

lines and equipotential lines (courtesy of John Wiley

and Sons 279)

overall solution. Appendix B contains details of the Methods of Fragments

based on Harr's (1962) explanation of Pavlovsky's work.

(3) Closed form solutions exist for simpler seepage conditions such as

flow to a fully penetrating well with a radial source (Muskat 1946). Seepage

problems associated with dams typically require approximate solutions because

of complicated flow conditions.

4-8
c. Numerical and Computer Methods.

acceptable approximations for the Laplace

EM 1110-2-1901

30 Sep 86

Computer models are used to make

equation in complex flow conditions.

The two primary methods of numerical solution are finite difference and finite

element. Both can be used in one-, two-, or three-dimensional modeling.

Several computer programs for these methods are available within the Corps of

Engineers (Edris and Vanadit-Ellis 1982).

(1) The finite difference method solves the Laplace equations by

approximating them with a set of linear algebraic equations. The flow region

is divided into a discrete rectangular grid with nodal points which are

assigned values of head (known head values along fixed head boundaries or

points, estimated heads for nodal points that do not have initially known head

values). Using Darcy's law and the assumption that the head at a given node

is the average of the surrounding nodes, a set of N linear algebraic equations with N unknown values of head are developed (N equals number of

nodes). Simple grids with few nodes can be solved by hand. Normally, N is

large and relaxation methods involving iterations and the use of a computer

must be applied. Appendix B provides details of this method.

(2) The finite element method is a second way of numerical solution.

This method is also based on grid pattern (not necessarily rectangular) which

divides the flow region into discrete elements and provides N equations with

N unknowns. Material properties, such as permeability, are specified for

each element and boundary conditions (heads and flow rates) are set. A system

of equations is solved to compute heads at nodes and flows in the elements.

The finite element has several advantages over the finite difference method

for more complex seepage problems. These include (Radhakrishnan 1978):

(a) Complex geometry including sloping layers of material can be easily

accommodated.

(b) By varying the size of elements, zones where seepage gradients or

velocity are high can be accurately modeled.

(c) Pockets of material in a layer can be modeled.

4-6. Graphical Method for Flow Net Construction. Flow nets are one of the

most useful and accepted methods for solution of Laplace's equation (Casagrande

1937). If boundary conditions and geometry of a flow region are known and can

be displayed two dimensionally, a flow net can provide a strong visual sense

of what is happening (pressures and flow quantities) in the flow region.

Equation 4-2, paragraph 4.4, is an elliptical partial differential equation

whose solution can be represented by sets of orthogonal (intersecting at right

angles) curves. One set of curves represents flow paths of water through the

porous media while curves at right angles to the flow paths show the location

of points within the porous media that have the same piezometric head. The

former are called flow lines, the latter equipotential lines. The flow net is

a singular solution to a specific seepage condition, i.e., there is only one

family of curves that will solve the given geometry and boundary conditions.

This does not mean that a given problem will have only one flow net--we may

choose from the family of curves different sets of curves to define the

problem, figure 4-5. The relationship between the number of equipotential

4-9
EM 1110-2-1901

30 Sep 86

drops, Nd , and flow channels, Nf , does not change. A brief study of

figure 4-5 will provide a feel for where quantity of flow is greatest,

velocity highest, and gradient highest, i.e., in the area of the porous soil

nearest the sheet pile (flow channel 4, figure 4-5(a); flow channel 5,

figure 4-5(b)). This section draws upon several publications which give

a. Net drawn for four flow

channels.

b. Net drawn for five flow

channels.

Figure 4-5. Flow net for a sheetpile wall in a permeable foundation

(from U. S. Army Engineer District, Little Rock92)

detailed explanation of flow net derivation and drawing instructions

(Casagrande 1937; Cooley, Harsh, and Lewis 1972; Soil Conservation Service

1973; and Cedergren 1977). One of the best ways to develop an understanding of

seepage and flow nets is to study well-drawn flow nets found in these and other

references and to practice drawing them.

a. Assumptions for Flow Net Construction. In order to draw a flow net,

several basic properties of the seepage problem must be known or assumed:

(1) The geometry of the porous media must be known.

(2) The boundary conditions must be determined (see paragraph 4.2).

(3) The assumptions required to develop Laplace's equation must hold

(see paragraph 4.4b).

(4) The porous media must be homogeneous and isotropic (anisotropic

conditions are dealt with in paragraph 4.7).

4-10
EM 1110-2-1901

30 Sep 86

b. Guidelines for Flow Net Drawing. Once the section of porous media

and boundary conditions are determined, the flow net can be drawn following

general guidelines:

(1) Determine flow conditions at the boundaries:

(a) Flow will be along and parallel to impermeable boundaries lines BCD

and FG, figure 4-5.

(b) Entrances and exits are equipotential lines, lines AB and DE,

figure 4-5, with flow perpendicular to them.

(c) Flow will be along and parallel to a line of seepage--line AB,

figure 4-6.

Figure 4-6. Seepage through an embankment

underlain by an impermeable foundation

(courtesy of John Wiley and Sons 155)

(d) Entrance and exit conditions for a line of seepage are shown in

figure 4-7 under "Conditions for Point of Discharge."

This will provide a feel for the flow net.

(2) Equipotential and flow lines must meet at right angles and make

curvilinear squares. Usually, it is best to make either the number of flow

channels a whole number (if the number of flow channels is a whole number, the

number of equipotential drops will likely be fractional).

(3) Generally, a crude flow net should first be completed and adjustments applied throughout the net rather than defining one portion since

refinement of a small portion tends to shift the whole net.

(4) The initial emphasis should be on getting intersections of flow

lines and equipotential lines at 90o, then shifting lines to form squares.

(5) If, in the finished flow net, either equipotential drops or flow

channels end up as a whole number plus a fractional line of squares (equipotential drop or flow channel), this should not be a problem but must be used

in any calculations based on the flow net. It is convenient to locate a partial equipotential drop in an area of uniform squares since this will make

accurate estimation of the fraction easier.

4-11
EM 1110-7-1901

30 Sep 86

Figure 4-7. Entrance and discharge (exit) conditions for a

line of seepage (courtesy of New England Waterworks

Association 151)

(6) Use only enough flow lines and equipotential lines to bring out

flow net definition. If more information is needed in particular areas, the

squares may be subdivided into smaller squares for more detail of flow and

pressure distribution.

(7) As shown in figure 4-6, equipotential line intersections at a line

of seepage, line AB, and a surface of seepage or discharge face, line BC, are

controlled by elevation since pressure is atmospheric along these lines.

Along the discharge face BC, the equipotential lines and flow lines do not

form squares since the discharge face is not a flow line or an equipotential

line but a line at atmospheric pressure and changing elevation potential.

(8) Figures 4-7 and 4-8 provide some guidelines for entrances and exits

and particular areas within the flow region.

4-12
EM 1110-2-1901

30 Sep 86

For foundations, furthermost upstream and downstream flow lines and equipotential lines should

intersect at or near the center of the pervious

foundation.

The flow line and equipotantial line nearest an

angle shouId intersect on the bisector of the

angle.

Same as (b) except for an upstream toe on an

impervious foundation.

2:1 length ratios to establish shape of the

“square” in a pervious foundation at the toe of

an impervious fill.

2:1 length ratios used with angle bisectors to

shape flow around an imbedded 90-degree angle.

2:1 length ratios to establish flow directions

beneath a thin cutoff wall taken to the midpoint

of the pervious stratum.

Subdivide to check odd-shaped "squares”. Resulting smaller odd-shaped "squares” should

have the general shape of the one subdivided.

Figure 4-8. Guides for flow net construction (from U. S. Department

of Agriculture 123 )

4-13
EM 1110-2-1901

30 Sep 86

(9) It is helpful to lay out the boundaries which will contain the flow

net in ink and use a soft pencil and eraser to develop the flow net to final

form.

(10) Accuracy of squares may be checked by drawing diagonals for a

square or subdividing the square by sketching an additional flow line and

equipotential line orthogonal to it (ad infinitum). The diagonals should be

smooth curves intersecting at right angles. Also, if the intersection of

two flow lines and two equipotential lines is a square, a circle, tangent to

each of the sides, may be inscribed within the square.

(11) For calculation of seepage quantity only a crude flow net is

required. Accurate flow nets are required to determine pressure distribution.

4-7. Flow Net for Anisotropic Soil. Most naturally occurring soils and many

man-placed soils have greater horizontal permeabilities than vertical. This

affects the shape of a flow net since the flow net provides a solution to

Laplace's equation which is based on the assumption of an isotropic porous

media (paragraph 4.4b). To compensate for anisotropy, the dimensions of the

porous media are changed by the square root of the ratio of the two permeabilities. If kh

permeability,

is the horizontal permeability and kv is the vertical

then the horizontal dimensions of the porous media cross section

are changed by a ratio of , e.g., if the base of a dam is 300 feet,

then it would be changed by a factor of , or would be 300 feet times

The same ratio would be applied to all other horizontal dimensions

to produce a transformed section. Next the flow net is drawn on the transformed section, as described in paragraph 4-6. Then the section, including the

flow net, is returned to the original (true section) which produces a nonsquare

flow net. Computations are made using the nonsquare flow net just as a square

flow net is used for isotropic conditions. This procedure is illustrated in

figures 4-9 and 4-10. In the same manner, dimensions in the vertical direction

could be changed by the factor , square or normal flow net drawn

on the transformed section, then returned to true section. Pore pressure

distribution and hydrostatic uplift may be taken from either section while

gradient and magnitude of seepage forces must be determined from the true

section.

4-8. Flow Net for Composite Sections. Commonly, projects requiring seepage

analysis involve different soils with different permeabilities, e.g., stratified foundation materials and zoned dams. Certain rules apply to flow lines,

equipotential lines, and lines of seepage crossing internal boundaries between

soils of different permeabilities. Figure 4-11 illustrates the deflection of

flow lines and equipotential lines at interfaces. The essential principle is

that the more permeable soil allows the same amount of water to flow with less

restriction, thus drops in potential within the higher permeability soil will

be farther apart (i.e., less energy loss in the higher permeability soil for

the same length of flow as in the low permeability soil). It should be noted

in figure 4-11 that when flow goes from lower permeability soil to higher

permeability soil, the distance between flow lines decreases (flow channel gets

smaller) and the distance between equipotential drops increases, Figures 4-12

through 4-14 are examples of flow net construction for seepage through soils of

4-14
EM 1110-2-1901

30 Sep 86

a. True section for kh

conditions.

= kv and transformed section for anisotropic

b. True section for flow net in a for kh = 4kv

c. True section for flow net in a for kh = 9kv

Figure 4-9. Flow nets constructed on transformed section and redrawn on true

section (courtesy of John Wiley and Sons 155 )

4-15
4-16

--------r---------1--------------

io 

,., u 

H 

.s=S 

luopcr vious hotnulnr y 

__ :}/ ______ -----

Stole (fl!ct 

----- ---

Anisotropic foundulion 

lch = 100 ky 

fJAM 

flow t honnel 

Notes• I. llorl,onlol Ira 

futtur 

2. k1= v'(ky)(lch 

3. Nrtu,, · 6.6!j 

4. q 

=7j 9k 

Noles• I. Toe mu 

to ol.lhJin vul 

2. 

Figure 4-10. Example of technique for developing a flow net for an anisotropic founda

123 U. S. Department of Agriculture ) 
4-17

= b I 

Interface 

k2 

d k.J 

c = k2 

tan 

tan 

----Flow lines 

---Equipotential lines 

Figure 4-11. Deflections of flow lines at interfaces of soils having dif

permeabilities (courtesy of New England Waterworks Association15.1) 
EM 1110-2-1901

30 Sep 86

a. Identify boundaries

b. Determine deflection of flow net at interface between soils with

different permeabilities.

c. Trial flow net

d. Final flow net

Figure 4-12. Flow net construction for a composite section

(courtesy of John Wiley and Sons155)

4-18
EM 1110-2-1901

30 Sep 86

a. Construct flow net assuming an impermeable foundation.

b. External equipotential lines into foundation without adjusting lines of net

in dam.

c. Adjust flow net until balanced.

Figure 4-13. Flow net construction for embankment on a foundation of lower

permeability (courtesy of John Wiley and Sons155)

4-19
EM 1110-2-1901

30 Sep 86

a. Construct flow net assuming impermeable embankment

b. Extend equipotentials up into dam locating initial position of

line of seepage

c. Adjust flow net to meet basic flow net requirements.

Figure 4-14. Flow net construction for an embankment on a foundation

of higher permeability (courtesy of John Wiley and Sons

155

)

4-20
EM 1110-2-1901

30 Sep 86

differing permeabilities. In all cases, flow lines and equipotential lines

maintain continuity across the interface between the soils though direction

will change abruptly. Additionally, the number of flow channels must remain

constant throughout the flow net. For the two examples of embankments with

foundations of differing permeabilities, figures 4-13 and 4-14, the flow is

more or less parallel to the interface, and the more permeable zone will

dominate flow location and quantity. Because of this, the flow net can be

started by assuming all flow goes through the most permeable zone. Once this

flow net is drawn, it is extended into the lower permeability zone and refined

to meet the general flow net criteria of paragraph 4.6. Transferring a line of

seepage across the interface of soils of differing permeability, such as in a

zoned dam, is more involved than transferring of flow lines and equipotential

lines and will be described in Chapter 6.

4-9. Determination of Seepage Quantities, Escape Gradients, Seepage Forces,

and Uplift Pressures. A flow net is a picture of seepage conditions under

given geometry and boundary conditions. It explains how pressures are distributed and where flow is being directed. Coupled with the knowledge of head

imposed on and the permeability of the porous media, the flow net can supply

important information about stability and flow quantity in two-dimensional

idealization of the real situation.

a. Seepage Quantities. Each of the complete flow channels passes an

equal volume of water per unit of time, while partial channels carry a proportional flow. Each of the complete potential drops between equipotential lines

is an equal portion of the total head, h , applied across the flow net with

partial drops having a proportionally smaller part. The number of flow channels, including any partial channel, is given the symbol Nf while the number

of equipotential drops, including any partial drops, is given the symbol Nd .

The ratio of Nf/Nd is called the shape factor, , which is a characteristic

of the given geometry and boundary conditions and permeability ratios (k1/k2,

kv/kh). Quantity of flow per unit length through the porous media can be

determined by using Darcy's law, q = kiA and the shape factor. Total flow is

the sum of the flows through each flow channel, i.e., q = where q

is the total flow and is the flow through each complete flow channel. In

figure 4-10, q = Since is the head loss between each

equipotential line (h = is the dimension of a flow net square:

and from the Darcy equation:

4-21
EM 1110-2-1901

30 Sep 86

where a is the area of the rectangle perpendicular to the flow direction.

If one side of the rectangle is one unit of length perpendicular of the plane

of the flow net, and the other dimension is , thus a = This

leads to:

Then:

which gives the quantity of seepage flow for each unit of thickness of porous

media perpendicular to the plane of the flow net. Figure 4-10(b) gives an

example of this calculation for anisotropic seepage conditions in a dam

foundation. The permeability, k' , used for anisotropic conditions,

k' = is derived by Casagrande (1937).

b. Escape and Critical Gradients. The escape or exit gradient, ie ,

is the rate of dissipation of head per unit of length in the area where

seepage is exiting the porous media. For confined flow, the area of concern is

usually along the uppermost flow line near the flow exit, e.g., at the

downstream edge of a concrete or other impermeable structure, figure 4-15.

Escape gradients for flow through embankments may also be studied by choosing

squares from the area of interest in the flow net (usually at or near the exit

face and downstream toe) and calculating gradients. If the gradient is too

great where seepage is exiting, soil particles may be removed from this area.

This phenomenon, called flotation, can cause piping (the removal of soil

particles by moving water) which can lead to undermining and loss of the

structure. The gradient at which flotation of particles begins is termed the

critical gradient, icr . Critical gradient is determined by the in-place

4-22
4-23

ttcad Water 

Ground ______ , __ _ 

-

Ol 

. 

w 

• 

·------·.-' Fu!l'l -- ---------- I desivnu!lon ol dropa fhwd lou • Upllll preasur t to point • flo. drops) ( IB.B'- hd.lon) Y. \!lj ___ (p_ s r I " 

5,5 5,1 85 5 

-----

6 5.6 824 

--- ---

7 6.5 768 

- ---

7,6 7.2 ___ 

---·--·-- --- -

E 

__ 

.. 

0.0 fl. 2 661 

--- -F---e 9.5 0.8 62 4 

Pnuure. 1lonu 111•1•P.r liniN IJ,.unriJrv 

lbollout ol w"h I 

'N 

. 

CP . GJ 

--

Ql 

(\) 

It 

E1cap1 gredlent 11 tocwoll end ''" s

Figure 4-15. Base uplift and escape gradient for concrete drop spillway 

(f U S f A . 1 123) rom • . Department o gr1cu ture 
EM 1110-2-1901

30 Sep 86

unit weight of the soil and is the gradient at which upward drag forces on the

soil particles equal the submerged weight of the soil particles, figure 4-16.

The critical gradient is dependent on the specific gravity and density of the

soil particles and can be defined in terms of specific gravity of solids, Gs ,

void ratio, e , and porosity, n :

since n

and e

or, e = 

1-n n=1+e

If typical values of Gs , e , and n for sand are used in the above

equations, ic r will be approximately 1. Investigators have recommended

ranges for factor of safety for escape gradient, FSG from 1.5 and 15,

depending on knowledge of soil and possible seepage conditions. Generally,

factors of safety in the range of 4-5 (Harr 1962, 1977) or 2.5-3 (Cedergren

1977) have been proposed.

c. Heave. In some cases, movement of soil at the downstream seepage

exit may not occur as flotation followed by particle-by-particle movement. A

mass of soil may be lifted initially, followed by piping. This phenomenon is

called heave and occurs when the upward seepage force due to differential head

equals the overlying buoyant weight of soil. Heave occurs under conditions of

critical hydraulic gradient. For field conditions, the point at which minimum

differential head offsets the overlying buoyant weight must be determined by

judgment and calculations. Terzaghi and Peck (1967) have evaluated the factor

of safety with respect to heave for a row of sheet piles. Resistance to heave

4-24
EM 1110-2-1901

30 Sep 86

Figure 4-16. Definition of critical gradient (prepared by WES)

may be developed by placing very pervious material on the exit face, which will

allow free passage of water but add weight to the exit face and thus add

downward force. This very pervious material must meet filter criteria to

prevent loss of the underlying soil through the weighting material.

d. Seepage Forces. Forces imposed on soil particles by the drag of

water flowing between them must be considered when analyzing the stability of

slopes, embankments, and structures subject to pressures from earth masses.

These forces are called seepage forces. The magnitude of this force on a mass

of soil is determined by the difference in piezometric head on each side of

the soil mass, the weight of water, and the area perpendicular to flow. The

4-25
EM 1110-2-1901

30 Sep 86

seepage force acts in the same direction as flow, i.e. along flow lines. Consider the seepage force on plane A-A in figure 4-16. Since flow is vertically

upward, the direction of seepage force is up, the difference in piezometric

head is h , and the area perpendicular to flow is A . The seepage force,

Fs , is the part of the upward forces due to differential head, h , or:

In terms of gradient and unit volume;

and using fS

as seepage force per unit volume:

Two methods of applying this force to use in stability analysis are described

by Cedergren (1977) and termed the gradient method and boundary pressure

method. EM 1110-2-1902 gives examples of embankment stability analyses

considering seepage forces. Additionally, the effect of buoyant forces on soil

mass stability must also be considered. The upward or buoyant force, Fb ,

causing reduction in effective stress on plane A-A, figure 4-15, is the

remainder of the upward forces on plane A-A:

e. Uplift Pressures. When seepage occurs beneath concrete or other

impermeable structures or strata, the underside of this impermeable barrier is

subject to a force which tends to lift the structure upward. The determination of this pressure or force is important in analyzing the stability of the

structure. An example of the analysis is given in figure 4-15. Summing of

the uplift pressures over the bottom area of the spillway will give the total

uplift force on the structure for a stability analysis. Harr's text (1962)

provides methods other than flow net construction to determine uplift

pressures.

4-26
EM 1110-2-1901

30 Sep 86

CHAPTER 5

CONFINED FLOW PROBLEMS

5-1. General Considerations. As explained in Chapter 4, confined flow exists

when the saturated pervious soil mass does not have a line of seepage boundary.

Impervious weirs or gravity dams on pervious soil or rock are typical projects

which have confined flow conditions. This chapter will consider two of these

cases. While examples of this chapter use flow nets, other methods for determining uplift and gradient such as the Method of Fragments may be used.

5-2. Gravity Dam on Pervious Foundation of Finite Depth. Figure 5-1, a copy

of figure 4-15, provides an example of an impervious structure on a pervious

foundation of finite depth with calculation of uplift and escape gradient.

Figure 4-12 illustrates a gravity dam on a composite pervious foundation of

finite depth and figure 4-10 shows an example of an impervious dam (though not

a gravity dam) on a finite anisotropic foundation. A cross section of a

classical gravity dam/weir, figure 5-2 indicates the effect of a partially

penetrating cutoff placed beneath the upstream portion of the dam. Comparing

figure 4-10(b) with figures 5-1 and 5-2 will show the reduction in gradient at

the downstream toe caused by embedment of the structure in the pervious

foundation. Embedment provides a longer upper flow line for a given structure

width and reduces the gradient at the downstream toe of the structure. Other

measures to reduce uplift and/or high gradients at the downstream toe include

cutoffs beneath the downstream portion of the dam and placement of drains

beneath the downstream portion of the dam.

5-3. Gravity Dam on Infinitely Deep Pervious Foundations. This case, illustrated by figure 5-3, is symmetrical (if there are no asymmetrical cutoffs or

drains beneath the dam) and at large distances becomes a series of half circle

arcs for flow lines and radial lines for equipotential lines. Since the upstream (entrance) and downstream (exit) boundaries extend to infinity and the

foundation depth is infinite , the flow quantity is infinite. Obviously the

analyst must decide the limits of the problem and calculate flow quantity

based on those limits. The same manipulations and effects of embedment, cutoff, and drain described for the previous case will apply to this case.

5-1
5-2

lleod Woler 

___ V..__ ________ --

Ground 

lrurrervious 

Uountlor y \ 

77.11111 I rrr I 11 

13.8; 

----

Porn! No. of drops 

desiqnotio11 to point 

A "5,5 

--·----

B 6 1---·-- ---·----

c 7 

f----·· ·------

0 l.8 

-- --

E 8.8 

-·---- --------

F 9.5 

Ueod loss : 

11\h a No drops) 

(fl.) 

5.1 

5.6 

6.5 

---·-

l.2 

8.2 

---- -- --

8.8 

Toil 

Uplift pressure 

( 18. a'- hd 0 loss) Y. 

(ps.U 

Escape yr adient at torwall and tramverse 

855 

824 

768 

724 

G61 62 'l 

··-

Figure 5-l. Base uplift and escape gradient for concrete drop spillway (fr

123 U. S. Department of Agriculture ) 
EM 1110-2-1901

30 Sep 86

Figure 5-2.

(courtesy of

Gravity dam on pervious foundation of finite depth

McGraw-Hill Book Company

181 )

Figure 5-3. Gravity dam on an infinitely deep pervious foundation

(prepared by WES)

5-3
EM 1110-2-1901

30 Sep 86

CHAPTER 6

UNCONFINED FLOW PROBLEMS

6-1. Introduction. This chapter will consider unconfined flow problems for

cases involving earth dams. Because of their ability to give a strong visual

sense of flow and pressure distribution, flow nets will be used to define seepage. Other methods, such as transformations (Harr 1962), electrical analogy

models, and numerical methods, can provide pressures and flows and be used to

develop flow nets. Unconfined flow problems require the solution of flow and

pressure distribution within the porous media and definition of the line of

seepage boundary (phreatic surface within the dam).

6-2. Homogeneous Earth Dam on Impervious Foundation. The simplest earth dam

configuration consists of a homogeneous, pervious embankment on an impervious

foundation. Though rarely encountered in engineered embankments, this case

will introduce general methods of defining flow in embankments.

a. Definition of Unknown Seepage Boundaries and Calculation of Flow per

Unit Length of Embankment, q . It is desired to define the flow and pressure

distribution within the embankment and total flow through the embankment. The

first step is determination of the upper flow line (which is the line of seepage boundary) and the length of the seepage exit face on the downstream slope

of the earth dam. This provides all necessary boundary conditions for flow

net construction and complete seepage definition. The two unknown boundaries,

BC and CD, figure 6-1, are a combination of an entrance condition, figure 4-7(c), BBl; part of a parabola, B1B2; a smooth transition between points

of tangency, B2C, and a straight line discharge face along the downstream

slope, CD. A parabola, shown by the dashed line, is the basic geometric member

used to define the location and extent of the two boundaries. Casagrande

(1937) provided the standard reference for flow through embankments while

others (Harr 1962, Cedergren 1977, and others) added to and refined the basic

methods. Figure 6-2 provides the nomenclature and formulas for drawing the

line of seepage and exit face and determining the quantity of seepage per unit

length of embankment, q . In a given problem, embankment geometry and head

water elevation provide values for h , m and which allow location of

points A and B and determination of distance, d , as shown in figure 6-2.

Figure 6-1. Line of seepage, BC, and seepage exit face, CD, for a

homogeneous earth dam on an impermeable foundation (prepared by

WES)

6-1
EM 1110-2-1901

30 Sep 86

Figure 6-2. Determination of line of seepage and seepage exit

face for embankments on impervious foundations (adapted from

New England Waterworks Association 151 )

6-2

h 

m 

I 

/I 

I I 

I I 

r I 

I I 

METHOD 

I SCHAFFERNAK -

VAN ITERSON 

; L. CASAGRANDE 

~ KOZENY 

A. CASAGRANDE 

-........ (' ........ . 

........................ 

X 

d 

. EQUATIONS 

! a = _d- - j d2 - h2 

I cos 0: cos2 0: ~ 

I k . 1 q • a sm o: tan 0: 

J 2 h2 a= S - S --- o o sin2 0: 

....... tl 

FOR a< 60°, USE S0 = ..j d2 + h2 . FOR 

! 60° <a< 90°, USE MEASURED S0 = Ac +CD 

i q = k a sin2 0: 

i Yo 1 I 2 2 · I a =- =- [ V d + h - d l 

I 0 2 2 I 

I I q = 2ka0 = ky0 

I DETERMINE (a+ L\a) AS THE INTERSECTION OF 

THE BASIC PARABOLA AND DAM SLOPE. THEN 

DETERMINE L\a FROM C VALUE ON FIG. 6-5. 

q = k a sin2 0: 

OR 

q = ky 0 = k ( J d2 + h2 - d ) 
EM 1110-2-1901

30 Sep 86

b. After this is done one of the four methods shown in figure 6-2 and

explained below can be used to determine the location of the exit face CD and

the line of seepage BC.

(1) < 30o Schaffernak-Van Iterson. The two formulas for this method

given in figure 6-2 assume gradient equals dy/dx and allow direct determination of a and q . Construction of basic parabola shown in figure 6-3 is

the first step in determining the upper line of seepage (Casagrande 1937).

From embankment geometry and headwater height, point A is located. d and y

are determined by scribing an arc, with radius DA through point E. Then the

point of vertical tangency of the basic parabola, F, is determined. Line AG,

parallel to the embankment base and horizontal axis of the parabola, is drawn

and divided into an equal number of segments (6 in the case in figure 6-3).

Line GF, the vertical tangent to the parabola, located at yo/2 from the

downstream toe of the embankment is divided into the same number of equal

segments as line AG. The points dividing line AG into segments are connected

with point F. The intersection of these lines with their counterpart lines

drawn from the points on line GF define the parabola. Thus the basic parabola,

dashed line A-F, is defined. The upstream portion of the line of seepage,

dotted line BH, is drawn by starting at point B perpendicular to the upstream

slope (since the upstream slope is an equipotential line and the line of 

seepage is a flow line) and continuing downstream to make line BH tangent to

the basic parabola at point H which is selected based on judgment. This is an

entrance condition as shown in figure 4-7. The central portion of the line of

seepage is along the basic parabola while the downstream portion is a smooth

transition from the basic parabola to tangency with the downstream slope at

point C. Point C is located a distance a. from the downstream toe as

determined by the equation for Schaffernak-Van Iterson shown in figure 6-2.

With all seepage boundaries known and using the rules of Chapter 4, a flow net

may be constructed within the boundaries as shown in figure 6-4. This figure

points out the important basic flow net requirement that all equipotential

lines intercept the line of seepage and exit face at points with equal vertical separation (in this case H/10 apart).

Figure 6-3. Construction of basic parabola (prepared by WES)

6-3
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30 Sep 86

Figure 6-4. Seepage through a permeable

embankment underlain by an impermeable

foundation (prepared by WES)

(2) < 90° L. Casagrande. The gradient assumption for this method is

i = dy/ds where s is the distance along the line of seepage, and allows

greater accuracy than Schaffernak-Van Iterson method for steeper downstream

slopes. Use of the equations in figure 6-2 and the same general procedures

used for the Schaffernak-Van Iterson method apply for up to 60o. For

60° < < 90°, since a and s are interdependent, the location of point C

(or distance a) must be estimated to determine the value of so

then distance a calculated. This procedure is repeated until there is

satisfactory agreement between the portion of the distance so as measured

and a as calculated. Thus the seepage boundaries are established allowing

flow net construction.

(3) = 180° Kozeny. For this special case Kozeny described a solution

adapted by Casagrande (1937). Figure 6-5 illustrates the nomenclature and

construction method for this case. Embankment geometry, h , and drain location control construction of the basic parabola. For this case the seepage

face is the distance a0 and the correction is not used. Again with

boundary definition, the flow net can be drawn.

(4) 30° < < 18.0° A. Casagrande. After study of model experiments

and construction of flow nets for various , A. Casagrande (1937)

developed a curve, figure 6-6, which relates a to the ratio,

Construction of the basic parabola is the first step in this procedure. The

point, Co , as shown in figure 6-2, where the basic parabola intercepts the

downstream slope is determined and distance a + is measured. Knowing

C can be found in figure 6-6 and calculated. Information is then sufficient to draw the line of seepage and discharge face, determine q , and construct the flow net. Casagrande (1937) provides a procedure for the condition

of tailwater on the downstream slope:

For the comparatively rare case in which the presence of tailwater must be considered in the design, the

determination of the line of seepage and of the quantity

can be performed by dividing the dam horizontally at tailwater level into an upper and lower section. The line of

seepage is determined for the upper section in the same

6-4
EM 1110-2-1901

30 Sep 86

Figure 6-5. Construction of basic parabola and seepage line for

= 180° Kozeny (courtesy of New England Waterways

Association151)

Figure 6-6. c vs (courtesy of New England

Waterworks Association151)

6-5
EM 1110-2-1901

30 Sep 86

manner as if the dividing line were an impervious boundary. The seepage through the lower section is determined

by means of Darcy's law, using the ratio of the difference

in head over the average length of path of percolation as

the hydraulic gradient. The total quantity of seepage is

the sum of the quantities flowing through the upper section and the lower section. The results obtained by this

rather crude approximation agree remarkably well with the

values obtained from an accurate graphical solution.

Harr (1962) explains an additional method, known as Pavlovsky's solution, for

determining a0 and q for the case of a homogeneous, pervious embankment on

an impervious foundation. Pavlovsky analyzed the embankment by dividing it

into three zones, writing an equation for q in each of the zones and, by

assuming continuity of flow, equating the three equations for q . Figure 6-7 provides the nomenclature for Pavlovsky's solution. The embankment is

divided as shown with Zone I between the upstream slope and a vertical line at

Figure 6-7. Nomenclature for Pavlovsky's solution

(courtesy of McGraw-Hill Book Company 180 )

the intersection of the crest and upstream slope (y axis), Zone II between the

y axis and a vertical line at the intersection of the line of seepage with the

downstream slope, and Zone III which is composed of the remainder of the

downstream toe. Pavlovsky assumed horizontal flow in each zone and wrote the

basic equation q for each zone using the nomenclature of figure 6-7.

The equations for each zone are:

Zone I

(6-1)

6-6
EM 1110-2-1901

30 Sep 86

Zone II

Zone III

for ho > 0

for ho = 0

(6-2)

(6-3)

(6-4)

It is assumed that a , , b , hd , hw , hO , and k are known for a

given problem, thus since qI = qII = qIII = q (continuity of flow, steady

state conditions) only a0 , h1 , and q are unknown. This analysis provides three equations, (6-1), (6-2), and (6-3), or (6-4), and three unknowns.

The equations may be solved in a number of ways. One method for ho= 0 is to

equate (6-1) and (6-4) and solve for a then equate (6-2) and (6-4) and solve

for a0 :

(6-5)

(6-6)

then a plot of ao versus h1 may be made of equations (6-5) and (6-6). The

intersection of the two curves representing (6-5) and (6-6) is the value of a0

and h1 for solution. Equation (6-4) will then provide q . An example from

Harr (1962) is provided in figure 6-8.

6-7
EM 1110-2-1901

30 Sep 86

Example: Determine the quantity of seepage, q , ao ,

Pavlovsky's solution for the dam shown above.

and h1 , using

Compare with

Schaffernak-Van Iterson and L. Casagrande Method, figure 6-2.

A. Pavlovsky's solution

For assumed values of h1

values for ao are given

the accompanying graph.

in equations (6-5) and (6-6) the resulting

in the following tabulation and plotted in

Equation (6-5) Equation (6-6)

h1 ao hl ao

50 19.6 50 15.9

52.5 18.7 52.5 17.7

55 17.4 55 19.7

60 13.9 60 24.1

65 8.4 65 29.3

Figure 6-8. Example problem of homogeneous embankment on

an impervious foundation comparing solutions (Continued)

(prepared by WES)

6-8
EM 1110-2-1901

30 Sep 86

From equation (6-4)

q =

0.002 ft/min 18.3 ft

3

= 0.0122 ft3/min per ft of embankment length

a = 3ao = 54.9 ft

B. Schaffernak-Van Iterson solution:

since m = 3(70 ft) = 210 ft

d = 0.3(210 ft) + 3(10 ft) + 20 ft + 3(80 ft) = 353 ft

hW = 70 ft

a = 73 ft

q = (0.002 ft/min)(73 ft)(sin 18°26')(tan 18°26')

q = 0.015 ft3

/min per ft of embankment length

C. L. Casagrande solution:

a = 76 ft

q = (0.002 ft/min)(76 ft sin2

 18o26')

q = 0.015 ft3

/min per ft of embankment length

Figure 6-8 (Concluded)

6-9
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30 Sep 86

6-3. Earth Dam with Horizontal Drain on Impervious Foundation. Figure 6-5

presents this case for a homogeneous embankment. However, since most earth

dams are built in horizontal layers, they very likely have a stratified

structure which may allow considerable flow to bypass the horizontal drain,

figure 6-9. The difference in vertical and horizontal structure also causes

differences in horizontal and vertical permeabilities. This can strongly

affect the location of the upper line of seepage, figure 6-10, which affects

stability considerations and methods of controlling seepage.

Figure 6-9. Schematic of effect of earth dam stratification on flow of

water through embankment with horizontal drain (prepared by WES)

6-4. Earth Dam with Toe Drain on Impervious Foundation. Toe drains are

another method of controlling the line of seepage, figure 6-11. Again the

effects of anisotropy must be considered, figure 6-12. The geometry of the

embankment and the toe drain, height of reservoir, and the degree of anisotropy

will control the location of the line of seepage.

6-5. Earth Dam with Vertical or near Vertical Horizontal Drains on Impervious

Foundation. One very effective method of intercepting horizontal flows due to

stratification of the embankment, figure 6-9, is the incorporation of an

inclined or vertical drain into the central portion of the embankment, figure 6-13. This seepage analysis of a zoned, anisotropic embankment assumed

the rockfill to have infinite permeability with respect to the core materials

and used the method recommended by A. Casagrande for drawing the parabola to

determine the upper line of seepage. The interface of the core and inclined

drain is used as the downstream slope for the seepage face since the drain has

a much higher permeability than the core material. Provision must be made in

sizing the drain to pass all the water coming out of the core without building

up a tailwater on the downstream slope of the core. It can be noted that the

designers of this example used m/3 instead of 0.3m to determine the interception point of the parabola and headwater elevation and the formula

which can be derived trigonometrically, to determine

The geometry of the embankment and toe drain, height of reservoir,

and the degree of anisotropy will control the location of the line of seepage.

6-6. Flow Net for a Composite Zoned Dam. If differences in permeabilities

between zones in a zoned dam are great enough (e.g. 100 to 1000 times or more)

the more permeable zone may be considered to have infinite permeability relative to the less permeable zone for purposes of seepage analysis. In the

seepage analysis example of figure 6-13 the upstream rockfill and the inclined

6-10
EM 1110-2-1901

30 Sep 86

Figure 6-10. Effect of difference in horizontal and vertical permeability

(anisotropy) on location of line of seepage within an embankment with a

horizontal drain (after U. S. Department of Agriculture123)

Figure 6-11. Homogeneous embankment on impervious foundation with a

toe drain (from EM 1110-2-191311)

Figure 6-12. Effect of anisotropy for homogeneous embankment

on impervious foundation with a toe drain (courtesy of New

England Waterworks Association151

)

6-11
6-12

TRANSFORMATION 

KH 4Kv, TRANSFORMATION r ='f'[ = _!.""' 0.5 v; 2 

TRANFORMEO SECTION HORIZONTAL DIMENSION= 0.5 TRUE SECTION HORIZONTAL DIMENSION 

DETERMINATION OF PHREATIC' LINE 

POOL OF SPILLWAY CREST E L 937', TAILWATER EL 8061, MAXIMUM NET HEAD" 1311 

ASSUMING TH!:. I::MEJANKMENT RESTS ON IMPERVIOUS FO\INOATIQN AS IN THE CASE 

OF THE LEFT ABUTMENT, THE POSITION OF THE PHREATIC LINt: IS DETERMINED AFTER 

A CASAGRANDE THE ABOVE ASSUMPliON PERTAINS TO THE DETERMINATION OF 

THE PHREATIC LINE ONLY WHICH LEADS TO MORE CONSERVATIVE DESIGN. 

Y 0 f( 156.96)2+!13l.OUI] -156 96 47.48' 

a•.la- TANa-2,tF2.a=63°-26",C05a-0.447 

= 85.86 -= 0 321AFTEA A. CASAGRANDE! 

..'IJ- 0 32 )( 85.86= 27. 48" 

£DAM 

I I 

GROUTING 

I 

TRUE SECTION EMBANKMENT SEEPAGE 

FOR NON-ISOTROPIC SOIL THE EFFECTIV

K' = KvKH, SINCE THE EMBANKMENT IMP

NON ISOTROPIC, K' = 6

K"- '(0"64 )( 10·6 CM•SEC = 0.8)( 10 6 CM'SE

SEFPAGE OUANTITY, q K H 

WHENH- 131FT, q/FOOT-1148)(10-9)( 1

Figure 6-13. Seepage analysis for Kettle Creek earth embankment, Kettle Creek, P

78 U. S. Army Engineer District, Baltimore ) 
6-13

£DAM 

I' 

MAX WATER SURFACE EL 962.7 " 

SPILLWAY CREST EL 937.0 

:TRANSFORMED SECTION 

FLOW NET 

LEFT ABUTMENT-STATION 17+00 

TRANSFORMATION 

fK; f1 1 KH • 4Kv. TRANSFORMATION FACTOR "i""i(,:; "j"4 • "2 • 0.5 

TRANFORMED SECTION HORIZONTAL DIMENSION • 0.5 TRUE SECTION HORIZONTAL DIMENSION 

DETERMINATION OF PHREATIC LINE 

POOL OF SPILLWAY CREST EL 937 1, TAl LWATER EL 8061, MAXIMUM NET HEAD • 131 1 

ASSUMING THE EMBANKMENT RESTS ON IMPERVIOUS FOUNDATION, AS IN THE CASE 

OF THE LEFT ABUTMENT, THE POSITION OF THE PHREATIC LINE IS DETERMINED AFTER 

A. CASAGRANDE. THE ABOVE ASSUMPTION PERTAINS TO THE DETERMINATION OF 

THE PHREATIC LINE ONLY WHICH LEADS TO MORE CONSERVATIVE DESIGN. 

y 0 • iH2+d2-d. il156.96)2+( 131.00)2 -156.96. 47.48' 

yo 

a+Jl.a = 1-COS a , TAN a • 2, a=2, a=63' -26', COS a • 0.447 

47.48 Jl.a a+Jl.a • 0_553 = 85.86; a+Jl.a • 0.32 (AFTER A. CASAGRANDE) 

l>a = 0.32 x 85.86 • 21. 48' 

Figure 6-13. 

EMBANKMENT SEEPAGE 

I 

:I: 

FOR NON-ISOTROPIC SOIL THE EFFECTIVE COEFFI

K' • KvKH, SINCE THE EMBANKMENT IMPERVIOUS 

NON ISOTROPIC, K' • oJKv KH • V10.4x1o-s) (1.6x1o-6

K' •I/Q.64 x 10-6 CM/SEC • O.Bx1o-6 CM/SEC OR 26.2

'N, 7 SEEPAGE OUANTITY,q/FOOT,•N K'H•l6 x 26.2

p 

WHEN H • 131FT. q/FOOT • 11.4Bx1o-9x 131 • 15.04 

Concluded 
EM 1110-2-1901

30 Sep 86

drain are considered infinitely permeable with respect to the central earth

portion of the embankment. In some cases dams may contain adjoining zones

which, have relatively small but marked differences in permeability and it may

be desired to accurately analyze the flow through these zones. Equipotential

lines and flow lines, with the exception of the upper line of seepage, will

cross the interface of the zones in the same manner as given for confined

composite sections in Chapter 4, but the location of the upper line of seepage

(phreatic line) must first be determined. Once its location is determined the

upper line of seepage transfers between regions of different permeabilities in

the manner shown in figure 6-14. In determining the location of the upper

seepage line, the essential principle to remember is that the flow rate must

be the same through each zone. That is, for a unit depth of embankment perpendicular to the plane of the flow net, Q must be the same for each zone.

More permeable zones require less gradient and/or cross-sectional area to pass

the flow transmitted to them from less permeable zones. This idea can be seen

in the example and instructions taken from Cedergren 1977.

Figure 6-14. Transfer of line of seepage between regions of

different permeability (courtesy of New England Waterworks

151 Association )

a. Locate the reservoir level and the tailwater level, noting the

difference in head as h and dividing h into a convenient number of equal

parts of increments Draw a series of light horizontal guide lines (head

lines) at intervals of across the downstream part of the section

(figure 6-15a).

6-14
EM 1110-2-1901

30 Sep 86

b. Guess a trial position for the phreatic line in both zones and draw a

preliminary flow net as shown in figure 6-15a, making squares in zone 1 and

rectangles in zone 2. Make the length-to-width ratios of all of the rectangles

in zone 2 approximately equal by adjusting the shape of the saturation line,

using an engineer's scale to measure the lengths and widths of the figures.

When this step is completed, the trial flow net should be reasonably well

drawn. It should satisfy the basic shape requirements of a flow net, but the

length-to-width ratio of the shapes in zone 2 probably will not satisfy

c/d = k2/k1 . Although the flow net has been drawn for a composite section,

the ratio of k2/k1 probably does not equal the k2/k1 ratio originally

assumed for the section.

a. First trial-flow net (not correct)

b. Completed flow net (correct)

Figure 6-15. Method for constructing flow nets for composite sections (courtesy of John Wiley and Sons 155)

c. Calculate the actual ratio of k2/k1 for the trial flow net just

constructed. To make this important check proceed as follows:

(1) Count the number of full flow channels between any two adjacent

equipotential lines in zone 1 and call this number nf-1. In the trial flow

net in figure 6-15a , nf-1 = 4.0 .

(2) Count the number of full flow channels between any two adjacent

equipotential lines in zone 2 and call this number nf-2 . In figure 6-15a,

nf-2 is equal to the width-to-length ratio of the figures in zone 2, d/c ,

and equal to 0.5.

(3) The actual value of k2/k1 for the trial flow net in figure 6-15a

can now be determined from the equation

6-15
EM 1110-2-1901

30 Sep 86

or

(4) If the calculated k2/k1 ratio is too high, the saturation line in

zone 2 is too low and must be raised. If the calculated k2/k1 ratio is too

low, the saturation line in zone 2 is too high and must be lowered. Raise or

lower the general level of the saturation line in zone 2 as indicated and

construct another trial flow net.

(5) Repeat steps (1) through (4) until a flow net of the desired

accuracy is obtained. (Usually a few trials will be sufficient.) By applying

the above equation to the first trial flow net in this example (figure 6-15a)

k2/k1 = 4.0/0.5 = 8.0. Because the ratio of k2/k1 for this example was

assumed to be 5, the k2k1 ratio of the trial flow net is too high; hence the

general level of the saturation line in zone 2 is too low and must be raised.

For the second trial flow net (figure 6-15b) nf-1 = 3.5 and nf-2 = 0.7 .

The calculated ratio of k2/k1 = 3.5/0.7 = 5.0 , the value originally assumed.

The above equation may be derived by recalling that the quantity of seepage in

zones 1 and 2 (figure 6-15) must be equal. Using

composite flow net being examined for accuracy. It is an essential criterion

to be used in constructing accurate flow nets for composite sections. Figure 6-16 illustrates the additional detail which can be obtained by further

subdivision of the flow net, This may be necessary for a stability analysis or

other reasons. Another example provided in figures 6-17 and 6-18 illustrates a

flow net for a zoned dam on an impervious foundation; figure 6-17 is the transformed section for the true section of figure 6-18 (Cedergren 1975 and U. S.

Army Engineer District, Sacramento 1977).

6-16
EM 1110-2-1901

30 Sep 86

Figure 6-16. Three forms of one flow net (courtesy of

John Wiley and Sons 155)

6-7. Zoned Earth Dam on Pervious Foundation.

a. Zoned embankments on pervious foundations may require rather involved

seepage analyses unless simplifying assumptions are made. This is particularly

true when relatively small permeability differences exist between adjacent

zones and foundation and it is desired to consider these differences in permeability. Figure 6-19 provides an example of such an analysis (U. S. Army Engineer Waterways Experiment Station 1956b). Development of the flow net required

use of a number of principles and methods explained in Chapter 4, and previous

portions of Chapter 6, e.g., dimensional changes due to anisotropy, upper seepage lines and other flow lines crossing the interface of materials having different permeabilities and composite sections. It should be noted that several

assumptions were made.

(1) The flow net for the foundation was drawn independently of the

embankment, i.e. considering the embankment to be impermeable, and assuming the

foundation to be isotropic.

(2) The embankment flow net reflects the influence of foundation flow

net in the location of equipotential and flow lines and is drawn for anisotropic conditions.

6-17
EM 1110-2-1901

30 Sep 86

Figure 6-17. Buchanan Dam flow net studies full reservoirSta 9+50 D/S transition fill - kh = 16 kv transformed

section (from Cedergren25 and U. S. Army Engineer District,

Sacramento 1977)

6-18
6-19

k-->oo 

EL 602 

H. R. CEDERGREN 

3-18-75 

BUCHAN

FLOW NE

FULL RESERV

DIS TRANSITION 

Figure 6-18. Buchanan Dam flow net studies full reservoir - Sta 9+50 

25 transition fill - = 16 kv true section (from Cedergren and U. S. 

Army Engineer District, Sacramento 1977)· 
6-20

650 

" z' 

'2 

500 

900 BOO 700 600 500 400 

( 

t<v = 2.5 K 10-8 CM/SEC ( _8 1<, Kh- 22.5 x 10-8 CM/SEC K 1 : 7.5 K 10 CM/SEC 

K (K" 10-B CMISEC ( K2 : 150 x 10-B CM/SEC 2 Kh .. 450 ._ t0-8CM/SEC 

K3 1 x 1 o- 4 CM/SEC K4 50 x 10-4 CM/SEC 

DISTANCE. FT FROM CENTER LINE OF DAM 

300 200 100 

SEEPAGE PER FOOT OF EMBANKMENT LE

0,. 1< 1 h S,. 7.5 X 10-8 CM/SEC X 192FT X 15/8 X 60 SEC/MIN X 1/30

0 a 0.00040 GAL/MIN PER FOOT OF EMBANKMENT 

FOR 600FT EMBANKMENT 

QTOTAL,. 600FT X 0.00040 GAL/MIN/FT E 0.24 GAL/MIN 

100 200 300 400 500 

NOTE. DIMENSION NUMBERS WIT 

FLOW NET INDICATE THE 

OF FLOW PATHS WITH REF 

TO 'THE CORE FLOW NET, 

• 

ROCK GROUT AND DRAIN ROCK TAI

a. IMPERVIOUS 

Figure 6-19. Seepage analysis, Blakely Mountain Dam, Arkansas (from U. S. Army 

121 Waterways Experiment Station ) 
6-21

660 

600 

500 

400 

... 

; 

t:aoo 

zo 

100 

-100 

COEFFICIENTS OF PERMEABILITY 

K1, K2, K3, AND K4 SAME AS ABOVE K5 = Kv • Kh= 5 x 1o-4 CM/SEC 

NOTE: DIMENSION NUMBERS WITHIN THE 

FLOW NET INDICATE THE NUMBER 

OF FLOW PATHS WITH REFERENCE 

TO THE C07 FLOW NET. 

b. PERVIOUS FOUNDATION 

Figure 6-19. Concluded 

SEEPAGE PER FOOT OF EMBAN

CleMBANKMENT "''R'1 h , ... 7.5 X 10-B CM/SEC X 192FT X 

X 7,48 GAL/FT3"' 0.00033 GAL/MIN 

OFOUNDATION • K5 h # • 5 X 10-4 CM/SEC X 192FT X 41

GAL/FT3 "' 0.66 GAL/MIN PER FOOT OF 

FOR 600 FT EMBANKMENT 

OTOTAL .. 600FT FT X (0.66 GAL/MIN/FT +0.00033 GAL/M

TAILWATER ASSUMED TO 

CONSTRucnON OF FLOW 

FOR CONSTRUCTION OF 

FOUNDATION, IT WAS AS

UPSTREAM COFFERDAM A

HIGH PERMEABILITY AND 

THE CORE AND RANDOM 

AFFECT THE FOUNDATIO
EM 1110-2-1901

30 Sep 86

(3) The flow nets were constructed assuming a tailwater elevation of

388 ft (approximate elevation of the base of the embankment) while seepage

quantities calculations assumed a tailwater elevation of 400 ft as shown on

the cross sections (i.e., h for calculation of Q is 192 ft).

(4) For calculation of Q in figure 6-19(b) the flow nets were considered to be separate but to have the same number of equipotential drops.

b. This example provides evidence that a large permeable member of the

embankment-foundation material controls the quantity of flow. In this case the

relatively impermeable embankment materials needed to be considered in order to

determine the upper seepage line, the extent of saturated materials, and the

expected pore pressures within the embankment. Seepage for this problem might

also be evaluated using a finite element computer program.

6-22
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CHAPTER 7

SEEPAGE TOWARD WELLS

7-1. Use of Wells. Wells are used in a variety of ways to control seepage.

They may be placed-on the landward side of water retention structures to

reduce pressure at the lower boundary of impervious strata. Wells are also

used to maintain dry conditions in excavations during construction. In

addition to seepage control, well pumping tests serve as an accurate means of

field determination of permeability (see Chapter 2).

7-2. Analysis of Well Problems. The graphical flow net technique described

in Chapter 4 or the approximate methods described in Appendix B can be used in

the analysis of well problems. However, formulas obtained from analytical

solutions to well problems are the most common methods of analysis.

a. Flow Nets. An example of a flow net for a simple flow problem is

shown in figure 7-1. The flow between flow lines is given by (Taylor 1948)

(7-1)

where

k = permeability (L/T)

= total head loss between equipotential lines (L)

r = distance from well (L)

b = dimension of element in Z direction (L)

= dimension of element in r direction (L)

As for a plan flow net, must be the same for all elements within

the net. Thus is a constant. When drawn in plan view (figure 7-1b)

the flow net consists of square elements as in the plane case described in

Chapter 4. When drawn in profile (figure 7-1c) the elements' aspect ratios

(b/R) are proportional to the radial distance r and are therefore not

squares. Thus, graphical construction of flow nets for radial flow problems

is generally not practical except for cases where the water bearing has a

constant thickness and only the plan view of the net is required.

b. Approximate Solutions. The numerical and analog methods described

in Appendix C can be used for problems involving complicated boundary conditions. Electrical analog methods are especially advantageous as most complicated well problems cannot be idealized in two dimensions.

7-1
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a. HORIZONTAL FLOW TO WELL

b. PLAN VIEW OF FLOWNET

c. PROFILE VIEW OF FLOWNET

Figure 7-1. Flowout of simple radial

flow problem (courtesy of John Wiley

and Sons268)

c. Analytical Formulas. The analysis of flow to a single well can

often be solved by analytical methods. Also, the analysis of flow to multiple

wells and many problems involving complicated boundary conditions can be

solved by superposition of solutions for single well problems. Analytical

solutions can be obtained for nonsteady flow problems.

7-3. Basic Well Equations for Steady State Flow. Steady flow conditions

exist when the well flow rate and piezometric surface do not change with time.

If the regional piezometric surface does not fluctuate, steady state conditions are achieved by pumping from a well at a constant rate for a long time

period. Design of wells for seepage control are often based on computations

assuming steady state conditions.

7-2
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a. Artesian Conditions. When significant flow to a well is confined to

a single saturated stratum, the problem can be idealized as shown in figure 7-2a. An artesian condition exists when the height h of the piezometric

surface lies above the top of the water bearing unit b . If the properties of

the soil are constant in all directions from the well, the discharge Q from

the well must be equal to the flow through a cylinder defined by the radius

r , height b , and differential thickness dr . Thus from Darcy's law

(equation 3-3), the flow can be written as

(7-2)

where

Q = constant discharge from well (L3/T)

k = coefficient of permeability -(L/T)

= hydraulic gradient along radius (L/L)

r = radius of cylinder (L)

B = thickness of aquifer (L)

Upon integrating equation 7-2, the relationship between r and h is found.

(7-3)

The constant can be determined by specifying that at the radius re , the

total head h is equal to a known head H , the total head that existed

before starting discharge from the well. That is,

(7-4)

Inserting equation 7-4 into equation 7-3, the constant term is found to be:

7-3
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a. HORIZONTAL AQUIFER CONFINED BETWEEN IMPERVIOUS STRATA

(ARTESIAN FLOW)

b. HORIZONTAL UNCONFINED AQUIFER (GRAVITY FLOW)

c. COMBINED AND CONFINED AND GRAVITY FLOW

Figure 7-2. Radial flow to horizontal aquifers (courtesy of

John Wiley and Sons 164

)

7-4
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By substituting the constant term into equation 7-3 and combining logarithmic

terms, the well equation for confined flow is obtained.

(7-5)

The distance re is often defined as the radius beyond which the well has no

influence or radius of influence.

b. Gravity Flow Conditions. Flow to a well under gravity (figure 7-2b)

differs from the confined flow problem in the important aspect that the height

B of the differential cylinder is equal to the variable h . Thus,

equation 7-2 must be written as:

(7-6)

which upon integration and substitution of boundary condition gives

(7-7)

The constant term can be evaluated from the condition at the radius of influence re as was done in equations 7-4 and 7-5. The constant term is given

by:

which when substituted back into equation 7-7 gives the well equation for

gravity flow

Development of equation 7-6 is based on the Dupuit assumption (Chapter 4)

which limits the applicability of equation 7-7 to those cases where the slope

of the piezometric surface is small (less than 5 percent). The error is

greatest in the vicinity of the well.

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c. Combined Artesian and Gravity Flow. When drawdown of the potentiometric surface becomes large near the well, combined gravity and confined conditions can occur (figure 7-2c).

d. Flow to Well Groups (Method of Superposition). The piezometric surface h caused by discharge from a group of wells can be determined by superimposing the solution for the individual wells given by either equation 7-3 or

7-6. For multiple wells, flow cannot be idealized by concentric cylinders and

the problem must be stated in terms of the plan coordinates x and y

(figure 7-3b). By noting that for a well located at

a general well equation can be written as

(7-8)

where

= potential required at point (x,y) to sustain a discharge Qi from

a well at

= hi (confined flow)

= (unconfined or gravity flow)

qi = intensity factor

( confined flow)

(unconfined or gravity flow)

Ci = constant

The head distribution can be determined by summing the individual

As the sum of the constants Ci is a constant, the multiple well

equation can be written as

(7-9)

where n is the number of wells. The constant is determined from a known

value of at a specified location. For example, the superposition formula

7-6
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a. FLOW BETWEEN TWO WELLS

b. COORDINATE SYSTEM FOR FLOW TO MULTIPLE WELLS

Figure 7-3. Flow to multiple wells (adapted from John Wiley

and Sons164)

7-7
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30 Sep 86

for the wells shown in figure 7-3 would be

At a distance re from both wells h(x,y) = H . The constant term is found

to be

Substituting the above equation into equation 7-9, the well formula for two

wells becomes

e. Hydrologic Boundaries (Image Well Method). When there are hydrologic

boundaries within the radius of influence of the well, equations 7-3 and 7-7

are no longer valid. Examples of boundaries are:

(1) A stream or river which can be idealized as a line source of equal

potential.

(2) A rock bluff line at the edge of an alluvial fill valley which can

be idealized as an impervious boundary.

The superposition of solutions (equation 7-9) can be used to analyze the flow

near a boundary by introducing an artificial device called an image well. An

image well is identical to the actual well and located symmetrically on the

opposite side of the boundary. The superimposed effect of the real and image

well for an infinite well is identical to the influence of the real well and

boundary. If the real well is a pumping well then a recharging image well is

used to represent boundaries such as rivers and a pumping image well is used

to represent an impervious barrier. For either case, the absolute value of

the flow Q for the image well is equal to that of the real well. For

7-8
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example, the head distribution created by a discharging well in the vicinity of

a river is identical to that created by the combined influence of a recharge

and discharge well (see figure 7-4). The head distribution created by the

discharge well in an infinite confined aquifer is given by

and by the image recharge well in the infinite aquifer

By superposition, the head distribution for the true actual problem is

(7-10a)

(7-10b)

(7-11)

Note that at the river rI = rR and Thus, constant = H , the

head at the river. Substituting the constant term into equation 7-11, the

formula for a single well near a recharge boundary is

To describe the head distribution for confined flow near an impervious boundary

an image discharge well is used (figure 7-4b), By the procedure used above, h

would be obtained as

(7-12)

7-9
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a. IMAGE WELL ANALYSIS OF DISCHARGE WELL NEAR

RECHARGE BOUNDARY (RIVER)

b. IMAGE WELL ANALYSIS OF DISCHARGE WELL NEAR

IMPERMEABLE BOUNDARY (ROCK BLUFF)

Figure 7-4. Application of image well method for analysis of flow

near boundaries (courtesy of Illinois State Water Survey 287

)

7-10
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The head at the impervious boundary is unknown, thus additional information is

needed to determine the constant. Note that when rR and rI are both equal

to the radius of influence that h = H . Thus

(7-13)

The image well method can also be applied to problems involving multiple

boundaries. For example, a common geologic situation involving multiple

boundaries would be a discharge well pumping from an alluvial terrace located

between a river and rock bluff (figure 7-5). In this case, the image well for

the river would have a second image well with respect to the rock bluff, which

in turn would have an image with respect to the river and so on. A similar

progression of image wells would be needed for the impermeable barrier.

Eventually, the location of each added-image well extends beyond its radius of

influence re from the pumping well and has no practical influence in the

solution.

7-4. Special Conditions. Although the simple well formula (equation 7-8) is

often used to analyze flow problems, it describes a relatively idealized condition that is found rarely in practice. It is generally desirable to consider the effects of partial penetration of wells, sloping aquifer, and

stratification of water bearing units in the analysis.

a. Partially Penetrating Wells. In deriving equations 7-3 and 7-7 it

is assumed that the flow lines are horizontal at the entrance of the well.

This assumption is valid only if the well completely penetrates the water

bearing strata. An approximate solution for flow to a well partially penetrating a confined aquifer was developed by Muskat (1946). The head can be

computed from

(7-14)

where C 1and C2

are constants to be determined from boundary conditions

is a function of the radius from the well (Warriner and Banks 1977).

The expression for given by Muskat (1946) was based on simplifying assumptions. Duncan (1963) and Banks (1965) assessed its validity from electrical

analogy model studies and developed a more accurate expression for The

alternative empirically determined relationship for developed by Duncan

(1963) is given in figure 7-6. The constants C1 and C2 are determined

7-11
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30 Sep 86

b. SECTION

a. PLAN

c. PRIMARY IMAGE

WELLS TO ACCOUNT FOR

INFLUENCE OF BOUNDARIES

ON REAL WELL

d. SECONDARY IMAGE WELLS TO

ACCOUNT FOR INFLUENCE OF

BOUNDARIES ON PRIMARY IMAGE

WELLS

Figure 7-5. Multiple image wells for a two-boundary problem

7-12
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30 Sep 86

Figure 7-6. Beta function curve (from Warriner and Banks

124 )

7-13
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30 Sep 86

from the boundary conditions at the well and at the radius of influence as

(7-15)

where

hw = total head at well (L)

= value of at well radius rw (dimensionless)

H = total head at radius of influence re (L)

The well discharge can be determined by using an empirically determined shape

(7-16)

with

where

b. Flows to Groups of Partially Penetrating Wells. An empirical method

developed by Warriner and Banks (1977) provides a means to modify the relationship obtained by superimposing solutions for individual fully penetrating

wells for the effects of partial penetration. First, the head at each well is

computed from the assumption that they fully penetrate the aquifer:

(7-17)

with

7-14
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30 Sep 86

where

hj = head at well j (L)

c = constant of integration (L)

Qi = discharge from well i (L3

/T)

k = coefficient of permeability (L/T)

B = aquifer thickness (L)

a = constant (L)

rij = distance between well i and well j (L)

rw j = radius of well j (L)

N = number of wells in group

In addition, the head at a point on the source boundary is given by:

where H is the head at the source and ris is the distance between

and the source. The drawdown at each well is computed from combining

equations 7-17 and 7-18

well i

with rjj = rwj .

(7-18)

(7-19)

Equation 7-19 gives the drawdown for each well within a group of fully

penetrating wells. The values of Qi required to cause the drawdown

can be determined by solving the system of N equations (7-19) for the N

unknowns Qi . As for the single well, a shape factor can be defined as:

(7-20)

7-15
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30 Sep 86

where is the shape factor for each well within a group.

factor can be corrected to account for partial penetration by

This shape

(7-21)

By replacing in equation 7-16 with the flow from the well group is

given as

(7-22)

The computations required to evaluate equations 7-19 through 7-22 are straightforward though they are time consuming for large well groups. Warriner and

Banks (1977) provide a FORTRAN code to compute discharge and drawdowns for

partially penetrating well groups within an arbitrarily shaped source boundary.

c. Wells in Sloping Aquifer. If the regional potentiometric surface

has a significant slope, the effect of superimposing the initial regional

gradient on the well drawdowns must be considered. For example, when pumping

from floodplain locations, the existing piezometric gradient from upland areas

to the river may be as great as those caused by pumping from the well. The

significant parameters for confined flow to a single well are shown in

figure 7-7. At a large distance from the well, the regional flow net would

not be affected. All flow into the well would be contained within the stream

lines separated by the dimension f . Thus by Darcy's law for one-dimensional

flow

where

Q = discharge from well (L3

/T)

k = permeability (L/T)

h1 = total head (L) for regional flow alone

(7-23)

7-16
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30 Sep 86

x = coordinate selected to be parallel to initial regional flow (L)

B = aquifer thickness (L)

f = width of flow lines enclosing all flow to well (L)

Figure 7-7. Superposition of well drawdown on regional gradient

(courtesy of International Institute for Land Reclamation and

Improvement199)

7-17
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The corresponding differential equation for the well would be

(7-24)

where

= total head due to flow to well

At a distance Xe downgradient from the well, a groundwater divide develops

(culmination point) at which

In view of equations 7-23 and 7-24

or

By substitution of equation 7-26 into equation 7-23

(7-25)

(7-26)

(7-27)

By integrating equations 7-24 and 7-27

(7-28)

7-18
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30 Sep 86

and superimposing the effects

(7-29)

The distance Xe can be removed from the expression by substitution of

equation 7-27

(7-30)

where i = the regional slope of the aquifer.

For conditions of unconfined flow, the regional gradient would be defined by a

parabola

which when combined with the well equations for unconfined flow gives

(7-31)

d. Layered Aquifers. Natural soils often occur in layers and a well

may penetrate units having different permeabilities. If flow to the well is

horizontal, the simple well equations can be used by assigning an average

value of permeability given by

where

km = horizontal permeability of layer m

dm = thickness of layer m

d = total thickness of layers

7-19

(7-32)
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30 Sep 86

Note that the permeability determined from a field pumping test is an average

of all units penetrated by the pumping well. A case where vertical flow can be

important is shown in figure 7-8. The discharging well is pumping from a

Figure 7-8. Flow to well with significant vertical flow through confining

layer (courtesy of John Wiley and Sons 164)

permeable unit overlain by a less permeable unit through which significant

vertical flow can occur. The flow to the well is given by

(7-33)

where

H = original total head (L)

h = total head at distance r from well at steady state condition

(L)

Q = discharge rate (L3

/T)

L = (leakage factor) (L)

B = thickness of aquifer

C = B'/k' (L)

B' = thickness of overlying low permeability unit (L)

7-20
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30 Sep 86

k ' = permeability of overlying low permeability unit (L/T)

= Hankel function (tabulated in table 7-1) (dimensionless)

7-5. Nonsteady State Flow. Nonsteady state flow may arise in several ways.

When pumping is started, time is required to establish a virtually steady state

condition. Flow during this period must be assumed to be nonsteady state. If

pumping occurs intermittently, a steady state condition may not be established.

Also, if large fluctuations occur at the source, potential steady state flow

conditions are not maintained. The steady state condition can be viewed as the

end condition that is reached after pumping for a long time period. In the

design of a well system for seepage control, it is generally adequate to

consider only the steady state condition. However, the determination of

coefficient of permeability from test data often requires analysis based on

nonsteady state condition. The duration of many well tests is too short to

Table 7-1. Values of Ko r/L for Selected Values of r/L to

Evaluation Equation 7-33 (a)

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

4.721

4.028

3.623

3.336

3.114

2.933

2.780

2.647

2.531

2.427 0.421

1.753 0.114

1.372 0.035

1.114 0.011

0.924 0.004

0.777 0.000

0.660 0.000

0.565 0.000

0.487 0.000

f = 10-2 f = 10-l

Example: = 0.5 , f = 10-1

 , K(0.5) = 0.924

f = 1.0

(a) Prepared from more extensive tables presented by Kruseman and De Ridder

(1970).

7-21
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reliably establish the steady state condition. Also, in practice, hydrologic

boundaries may be present within the steady state radius of influence. In

either case the use of the steady state flow equations could lead to substantial error in determining the permeability.

a. Nonsteady State Confined Flow. Theis (1935) developed the following

relationship for nonsteady state flow in a confined aquifer (Davis and DeWeist

1966):

(7-34)

where

Q = constant discharge rate (L3/T)

k = permeability (L/T)

B = thickness of aquifer (L)

W(u) = function given in table 7-2

The parameter u is given by

(7-35)

where

r = radius from well (L)

S = storage coefficient (dimensionless)

t = time from start of pumping (T)

The storage coefficient S represents the amount of water removed from storage as a result of consolidation of the aquifer and expansion of water in

response to the decline in head. Physically S is given by

(7-36)

7-22
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Table 7-2. Values of W(u) for Selected Values of 1/u

to Evaluate Equation 7-34 (a)

1 1 W(u)

f u f = 1.0 f = 2.0 f = 8.0

10-1 0.000 0.001 0.146

1 0.219 0.600 1.623

10 1.823 2.468 3.817

102 4.034 4.726 6.109

103 6.332 7.024 8.410

104 8.633 9.326 10.71

105 10.94 11.63 13.02

106 13.24 13.93 15.32

107 15.54 16.23 17.62

108 17.84 18.54 19.92

10g 20.15 20.84 22.22

1010 22.45 23.14 24.53

1011 24.75 25.44 26.83

1012 27.05 27.75 29.13

1013 29.36 30.05 31.44

1014 31.66 32.35 33.74

Example : u = 0.005 , = 200 , f = 2 , W(u) = 4.726

(a) Prepared by WES.

7-29
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30 Sep 86

where

= mass density fluid (m/L3)

g = acceleration of gravity (L/T2

)

B = thickness of aquifer

= bulk compressibility of aquifer (LT2/M)

n = porosity (dimensionless)

= bulk compressibility of fluid (LT2/M)

The determination of the aquifer properties kb and S from equation 7-34

requires a complete drawdown versus time history for each observation

piezometer. The Theis method for data analysis is based on the logarithmic

representation of equations 7-34 and 7-35

From the equations above it is seen that if Q is constant that log(H - h)

varies with log(r2

/t) in the same way as log [W(u)] varies with log (u)

regardless of the units used. Therefore, it should be possible to superimpose

the data curve on the theoretical curve because the two curves are offset from

each other only by the constant terms log and log S/4kB . By determining the value of the offsets from the superimposed curves, kb and S can

be determined. The computation consists of the following steps:

(1) A plot is made of W(u) (log scale) versus u (log scale). This

plot is referred to as the type curve.

(2) For each observation well, a plot is made of drawdown H - h (log

scale) versus (log scale).

(3) Superimpose the test data over the type curve in such a way that

the drawdown data best fit the type curve (figure 7-9). The coordinate axes

of the two curves should be kept parallel.

(4) Determine the values W(u) , u , H - h , and r2/t from an

arbitrarily chosen matching point on the two curves.

7-24
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Figure 7-9. Use of type curve for analysis of nonsteady state flow

(courtesy of John Wiley and Sons 164 )

(5) Compute the value of kB from equation 7-34 using the matching

point value of H - h and W(u) . Compute the value of S from equation 7-35 using the matching point values of u and r

2

/t combined with the

previously computed value of kB . The above procedure is carried out for

each observation well. Ideally, the computed values of kB and S should be

the same for all observation wells. Differences in the computed values may be

caused by geologic variations in the aquifer and hydrologic boundaries not

accounted for in the analysis.

b. Simple Method for Coefficient Determination (Jacob's Method). Jacob

(1950) introduced a simplification to the determination of kB and S by

noting that for small values of u (small r and/or large t) equation 7-34

reduces to (Davis and DeWeist 1966)

7-25
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30 Sep 86

(7-37)

Equation 7-37 can be written in a form convenient for graphical solution by

substituting equation 7-35 and writing in terms of base 10 logarithms:

(7-38)

From equation 7-38 it is seen that the relationship between drawdown H - h

and time t for a particular observation piezometer (r = constant) can be

represented as a straight line on a plot of H - h versus log t

(figure 7-10). The slope of the line is equal to Also, the time,

to , corresponding to H - h = o gives

which can be used to determine S . An alternative analysis consists of plotting H - h versus log r . The following relationship can be obtained by

rearranging the term in equation 7-38.

Equation 7-39 defines a straight line on a plot of H - h versus r

(figure 7-10b). The slope of the line is - and can be used to

determine kb . The line intersects the H - h = o axis at ro . This

intercept can be used to determine S from

(7-39)

Note that ro represents the radius of influence for the well at time equals

t . Thus the radius of influence for the steady state condition re is equal

to ro as t tends to infinity. This implies that the radius of influence

7-26
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30 Sep 86

a. One observation well

b. Simultaneous observations

Figure 7-10. Use of Jacob approximation for nonsteady state flow

(courtesy of John Wiley and Sons 164 )

7-27
EM 1110-2-1901

30 Sep 86

expands indefinitely and cannot be defined. However, the value of r

e

selected has a relatively small influence on computed drawdowns near the well

and equation 7-39 can be used to determine reasonable values for re .

Yield).

c. Nonsteady Unconfined Flow with Vertical Gravity Drainage (Delayed

Initial response (generally after first few minutes of pumping) is

given by (Kruseman and DeRidder 1970)

(7-40)

where

SA = storage coefficient for instantaneous release of water from

storage

W(uA , r/B) = Boulton well function (figure 7-11a)

r/B = formation constant to be determined from piping test data

Later time response is given by

where

Sy = specific yield

W(uy , r/B) = delayed yield well function

The application of equations 7-40 and 7-41 through use of a type-curve is

similar to that of equation 7-34. The following should also be noted:

(7-41)

(1) Type curves for several values of r/B should be plotted. The

curve giving the best fit to the initial time-drawdown data is used to

estimate r/B .

7-28
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30 Sep 86

a FAMILY OF BOULTON TYPE CURVES: W (UA,

1/Uy FOR DIFFERENT VALUES OF r/B.

r/B) VERSUS 1/uA AND W (Uy, r/b) VERSUS

a. Family of Boulton type curves:

W(Uy/r/b) versus 1/Uy

W(UA , r/B) versus 1/uA and

for different values of r/B

b. Boulton's delay index

curve

Figure 7-11. Type curves for Boulton's analysis of nonsteady unconfined

flow with delayed yield (courtesy of International Institute for Land

Reclamation and Improvement199)

7-29
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30 Sep 86

(2) The time-drawdown data overlay may be moved to obtain the best fit

for the latter time-drawdown data. Both initial time and latter time fits

should give the same value of r/B and kB .

(3) Eventually, the effects of vertical gravity drainage become negligible and the latter time curve merges with the Theis curve. The timecoordinate where the two curves merge is determined from Boulton's delay-index

curve (figure 7-11b).

(4) A number of type-curve solutions to the problem of nonsteady unconfined flow to wells have been developed (Fetter 1980). For example, Neuman

(1975) presented a type-curve method similar to Boulton's that accounts for

anisotropy of the aquifer.

d. Nonsteady Confined Flow with Vertical Drainage Through Confining

Layer (Leaky Aquifer). The leaky aquifer equation for nonsteady flow is based

on the assumptions that flow to the well is horizontal and vertical flow is

restricted to seepage through the confining layer. These assumptions are

identical to those made for the steady state case described by equation 7-33.

The drawdown is given by

where

r

2

S

u=4kBt

r = radius from well (L)

S = storage coefficient (dimensionless)

k = permeability (L/T)

t = time from start of pumping (T)

L = leakage factor (L) =

B = thickness of aquifer (L)

B ' = thickness of confining unit (L)

k' = permeability of confining unit (L/T)

(7-42)

W(u , r/L) = well function given in figure 7-12

7-30
7-31

1.0 

1.5 

----------2.0 

NONEQUILIBRIUM 

TYPE CURVE 

0 3 0.2 0.15 

·0 5°.4 . 

o.s-· 

0.8 

5"' 

u= 

0 0.0 .1 0.075 .05 

1 14.6 OW!u, r/Bl 

T 

2100 ,-2s 

Tt 

r /8= vT /IK'/b') 

10- 1 1.0 10 lol 103 104 105 10

1/u 

Figure 7-12. Type curve for nonsteady flow in a semiconfined aquifer (courte

164 John Wiley and Sons ) 
EM 1110-2-1901

30 Sep 86

The application of the type curve method for the leaky aquifer problem is similar to the application to the delayed yield problem. The time-drawdown data

are matched to the standard type curve with the curve giving the best fit being

used to estimate r/B .

e. Nonsteady Unconfined Flow with Little Vertical Drainage. If the

delayed response component of the drawdown is small, the Theis equation

(equation 7-34) can be used to analyze the flow by inserting a "corrected"

drawdown into the flow equation. The corrected drawdown is given by

(7-43)

f. Nonsteady Flow with Hydrologic Boundaries. The method of superposition presented for steady-state flow problems (equation 7-9) is applicable

to nonsteady flow problems. Therefore, the image well method can be used to

investigate the effects of hydrologic boundaries. For example, the image well

analysis for a discharging well near a river (recharge boundary) is (Davis and

Dewiest 1966)

where

rR

= radius from real well (L)

rI = radius from image well (L)

k = coefficient of permeability (L/T)

S = storage coefficient (dimensionless)

(7-44)

B = aquifer thickness (L)

t = time from start of pumping (T)

7-32
EM 1110-2-1901

30 Sep 86

Note, then, when the function W(u) can be replaced with a logarithmic

approximation, as in the Jacob's method (equation 7-37), equation 7-44 can be

approximated as

(7-45)

From equation 7-45 it is seen that as u becomes small, flow becomes virtually

steady state (compare equation 7-45 with the steady state case, equation 7-11).

Thus the presence of a recharge boundary in an aquifer tends to shorten the

time needed to reach steady state (Davis and Dewiest 1966).

7-33
EM 1110-2-1901

30 Sep 86

CHAPTER 8

SEEPAGE CONTROL IN EMBANKMENTS

8-1. General. All earth and rock-fill dams are subject to seepage through

the embankment, foundation, and abutments. Seepage control is necessary to

prevent excessive uplift pressures, instability of the downstream slope, piping through the embankment and/or foundation, and erosion of material by

migration into open joints in the foundation and abutments. The purpose of

the project, i.e., long-term storage, flood control, etc., may impose limitations on the allowable quantity of seepage.

8-2. Methods for Seepage Control. The three methods for seepage control in

embankments are flat slopes without drains, embankment zonation, and vertical

(or inclined) and horizontal drains.

8-3. Flat Slopes Without Drains. For some dams constructed with impervious

soils having flat embankment slopes and infrequent, short duration, high

reservoir levels, the phreatic surface may be contained well within the downstream slope and escape gradients may be sufficiently low to prevent piping

failure. For these dams, when it can be assured that variability in the

characteristics of borrow materials will not result in adverse stratification

in the embankment; no vertical or horizontal drains are required to control

seepage through the embankment. A horizontal drain may still be required for

control of underseepage (see Chapter 9). Examples of dams constructed with

flat slopes without vertical or horizontal drains are Aquilla Dam, Aubrey Dam,

and Lakeview Dam (U. S. Army Engineer District, Fort Worth 1976a, 1976b, 1980).

Figure 8-1 shows the analysis of through embankment seepage for Aubrey Dam, 

Texas (now called Ray Roberts Dam). As shown in figure 8-1a, this is a zoned

embankment with relatively flat slopes due to a weak stratum in the foundation. The slopes could be steepened from IV:10.6H to lV:8H if the weak foundation gains shear strength due to consolidation during construction (the dam

is scheduled for completion in 1988). A 3-ft-thick horizontal drainage blanket

and collector system will be provided under the downstream embankment from

sta 136+00 to sta 142+60 to control any seepage through the foundation. For

the analysis of through embankment seepage, shown in figure 8-1b, the steady

state phreatic surface was developed graphically for the conservation pool by

considering a homogeneous nonisotropic embankment and an impervious foundation.

Since the escape seepage gradients were computed to be less than 0.3 to 0.4

(see paragraph 4.9b), it was concluded that no vertical or horizontal drains

were required.

8-4. Zoning Embankments.

a. General. Embankments are zoned to use as much material as possible

from required excavation and from borrow areas with the shortest haul distances and the least wastage and at the same time maintain stability and control seepage. The different zones of an embankment are shown in figure 8-2.

For most effective control of through seepage and seepage during reservoir

drawdown, the permeability should progressively increase from the core out

toward each slope as shown in figure 8-2 (EM 1110-2-2300).

8-1
8-2

EL 511.0 

.--

UPSTREAM 18" RIPRAP ON 6 

SELECT 

IMPERVIOUS 

FILL 

ct_ EMBANKMENT 

I 

44' 

DOWNSTREAM 

3' HORIZONTAL DRAINAGE BLANKET ST. 

Figure 8-1. 

(from U. S. 

UPSTREAM 

FLOODPLAIN EMBANKM'NTSECTION 

STATION 100+00 TO STATION 142+25 

SCALES 

... 

HORIZONTAL 

30 0 30 60FT 

MW 

a. FLOODPLAIN EMBANKMENT SECTION 

£EMBANKMENT 

FLOODPLAIN EMBANKMENT 

50 100FT 

... 

b. EMBANKMENT SEEPAGE ANALYSIS 

DOWNSTREAM 

LEGEND 

KH =HORIZONTAL PERMEABILITY 

Kv PERMEABILITY 

Analysis of through embankment seepage for Aubrey Dam, 

81 Army Engineer District, Fort. Worth ) 

Texa
EM 1110-2-1901

30 Sep 86

Figure 8-2. Different zones of an embankment (prepared by WES)

b. Impervious Zone or Core. The purpose of the core is to minimize

seepage losses through the embankment. As a general rule, sufficient impervious material is available to result in small seepage losses through the

embankment. Therefore, the quantity of seepage passing through the foundation

and abutments may be more significant than the quantity passing through the

core. Important material properties of the core are permeability, erosion

resistance, and cracking resistance. A core material of very low permeability

may be required when the reservoir is used for long-term storage. A core

material of medium permeability may be utilized when the reservoir is used for

flood control. The erosion resistance of core material is important in evaluating piping potential (Arulanandan and Perry 1983). The tensile strength of

the core material is important in evaluating the cracking resistance

(Al-Hussaini and Townsend 1974). In general, the base of the core or the cutoff trench should be equal to or greater than a quarter of the maximum difference between reservoir and tailwater elevations (U. S. Army Engineer District,

Mobile 1976, EM 1110-2-2300). A core top width of 10 ft is considered to be

the minimum width on which earth-moving and compaction equipment can operate.

The maximum core width is controlled by stability and by availability of material. The top of the core should be above the maximum reservoir elevation

8-3
EM 1110-2-1901

30 Sep 86

but below the bottom of the frost zone, A vertical core located near the

center of the dam is performed over an inclined upstream core because the

former provides higher contact pressure between the core and foundation to

prevent leakage, greater stability under earthquake loading (Sherad 1966,

1967), and better access for remedial seepage control. An inclined upstream

core allows the downstream portion of the embankment to be placed first and the

core later and reduces the possibility of hydraulic fracturing (Nobari, Lee,

and Duncan 1973).

c. Filter Zones. Filters may be required in various locations in earth

dams such as vertical (or inclined) and horizontal drains within the downstream section of the embankment as shown in figure 8-2, around outlet conduits passing under the downstream portion of the embankment, under concrete

structures such as stilling basins, around relief wells, beneath riprap where

drawdown may occur, and between the embankment and abutment. Important properties of the filter material are gradation, compacted density, and permeability. Filters are designed to permit free passage of water and prevent migration of fines through the filter as discussed in Appendix D. The average

in-place relative density of the filter should be at least 85 percent and no

portion of the filter should have a relative density less than 80 percent

(EM 1110-2-2300). This requirement applies to vertical (or inclined) and

horizontal drains and filters under concrete structures but not to bedding

layers under riprap. Special care must be taken to assure that compaction does

not degrade the filter material (by grain breakage and/or segregation) and

reduce its permeability. When the filter material is sand or contains significant portions of sand sizes, the material should be maintained in as saturated

a condition as possible during compaction to prevent bulking. The discharge

capacity of the filter zones should be determined in dimensioning the filters

(Cedergren 1977). The filter material should pass the 3-in. screen for minimizing particle segregation and bridging during placement. As discussed previously in Chapter 2 (see figure 2-12), the permeability of sands and gravels

varies significantly with the amount and type of fines (material smaller than

the No. 200 sieve) present. Also, the amount and type of fines present

influence the capacity of a filter to self-heal by collapsing any cracks within

the filter (see figure 8-3). Therefore, the maximum percent fines and type

(silt, clay, etc.) to be allowed in the filter of an earth dam must be shown

to be sufficiently pervious by laboratory filter tests (1) and self healing by

collapse tests (Vaughn 1978). If vibration is present, such as in the vicinity

of a stilling basin or powerhouse, the. laboratory filter tests should be conducted with vibration effects. If the base material to be protected is

dispersive, large-scale box filter tests will be required (McDaniel and Decker

1979, Bordeaux and Imaizumi 1977, and Logani and Lhez 1979). The procedure to

use in identifying dispersive clays is given in EM 1110-2-1906. Generally, two

or more filter zones, each with a uniform or narrow gradation (sand, pea

gravel, etc.) are preferable to a single well-graded filter zone which often

becomes segregated during processing, stockpiling, and placement. Care must

(1) Laboratory filter tests are not a routine laboratory test. Standard testing procedures have not been developed. The conduct of laboratory filter

tests should be under the direction of a specialist and should be carried

out in a research laboratory.

8-4
EM 1110-2-1901

30 Sep 86

a. Self-healing (by collapse) of filter

b. Laboratory test for ability of filter material

to self-heal (by collapse)

Figure 8-3. Self-healing (by collapse) of crack

within a filter downstream of a core (courtesy

of American Society of Civil Engineers 282

)

be taken during construction to prevent reduction in permeability of the filter

by intrusion of fines carried by surface runoff, spillage by compaction equipment, or degradation during compaction. Also, care must be taken to prevent

coarse material from rolling down the surface of the filter and collecting

between the core and filter (or between filter zones if two or more filters are

used) forming a "tube" (in cross section) of more permeable material through

which core (or filter) material could be lost by piping.

8-5
EM 1110-2-1901

30 Sep 86

d. Transition Zones. The purpose of transition zones is to separate

zones of different permeability and compressibility within the embankment, to

prevent core material from being drawn into the upstream shell during rapid

drawdown of the reservoir, to provide a source to feed material into a crack

in the core and preventing piping (see figure 8-4). Important material

properties of the transition material are angularity of particles (upstream of

core, rounded particles and better for feeding material into cracks and preventing piping), gradation, permeability, and compressibility. Transition

zones may be located both upstream and downstream of the core and generally

have a width >10 ft. Wide transition zones between the filter and the downstream shell will control the rate of flow through a crack in the core and

extending through the filter in the event that self-healing (by collapse) of

the filter does not occur. Transition zones (and filter zones) should be

widened near abutments where tension zones may induce cracking.

Figure 8-4. Crack stopping transition upstream of a core

(prepared by WES)

e. Random Zones. The purpose of random zones is to utilize required

excavation. Random zones are assumed to have the properties of the least

desirable material in the excavation. Random zones may be located either

upstream or downstream of the core. For most effective control of through

seepage and seepage during reservoir drawdown, the more pervious material

should be routed to the outer portions of the embankment.

f. Cuter Zones or Shells. The purpose of the outer zones or shells is

to permit steeper embankment slopes. Important material properties of the

shell material are durability (soundness) of rock, gradation (well-graded),

and permeability (free-draining). The upstream shell affords stability

8-6
EM 1110-2-1901

30 Sep 86

against end of construction, rapid drawdown, and earthquake loading. The

downstream shell acts as a drain and controls the line of seepage and provides

stability under high reservoir heads. When suitable materials are not available for pervious downstream shells, control of seepage through the embankment

is provided by vertical (or inclined) and horizontal drains.

g. Upstream Drawdown Blanket. The purpose of the upstream drawdown

blanket is to provide stability of the upstream slope during rapid drawdown of

the reservoir. Important material properties of the upstream drawdown blanket

are durability (soundness) of rock and permeability (free-draining). Figure 8-5 shows the improvement in the factor of safety resulting from the

Figure 8-5. Improvement in factor of safety

resulting from the upstream drawdown blanket

(courtesy of John Wiley and Sons155)

8-7
EM 1110-2-1901

30 Sep 86

upstream drawdown blanket (Cedergren 1977). The required minimum permeability

of the upstream drawdown blanket can be calculated from (Cedergren 1977):

where

kmin = minimum permeability of the upstream drawdown blanket

vd d = velocity of drawdown of the water surface in the reservoir

L = defined in figure 8-6

n e = effective porosity of the upstream drawdown blanket

h = defined in figure 8-6

= angle between the median flow line in the upstream drawdown

blanket and the horizontal

The ratio h/L should not exceed 10.

(8-1)

Figure 8-6. Computation of required minimum permeability of the

upstream drawdown blanket (courtesy of John Wiley and Sons 155 )

8-5. Vertical (or Inclined) and Horizontal Drains.

a. Need. As stated previously, vertical (or inclined) and horizontal

drains may be required to control seepage through the embankment by preventing

material eroded through a crack in the core from washing into the downstream

shell by seepage water under reservoir head. Also, because of the often

variable characteristics of borrow materials, it is frequently advisable to

provide vertical (or inclined) and horizontal drains within the downstream

section of the embankment, as shown in figure 8-7, to ensure satisfactory

seepage control. For a stratified soil, the vertical permeability is

8-8
EM 1110-2-1901

30 Sep 86

a. HORIZONTAL DRAIN ONLY

b. INCLINED AND HORIZONTAL DRAINS

Figure 8-7. Use of inclined and horizontal drains to ensure seepage

control against variable characteristics of borrow materials

(courtesy of John Wiley and Sons 155)

controlled by the least permeable layer. Therefore, the horizontal permeability is always greater than the vertical permeability. Compacted soils in earth

dams are stratified due to variability in the characteristics of borrow materials and the tendency for soil particles to align horizontally during compaction. The ratio of vertical to horizontal permeability may range from 2 to 10

or greater. For stratified soils, as shown in figure 8-8, a horizontal drainage blanket is not sufficient to prevent the downstream slope from becoming

saturated and susceptible to piping and/or slope failure. However, when a

properly designed and constructed inclined drain and horizontal drain is used,

as shown in figure 8-8, complete control is provided over seepage through the

embankment.

b. Filter Requirements. Vertical (or inclined) and horizontal drains

should be designed as filters (see Appendix D). If crushed rock is used for

the drain material (see paragraph 2-2.g), material to be protected is dispersive, or material to be protected contains cracks, filter tests will be

8-9
EM 1110-2-1901

30 Sep 86

KH = KV

KH = 9KV

KH = 9KV

Figure 8-8. Effect of anisotropy of permeability on seepage through

earth dam with and without an inclined drain (courtesy of John Wiley

and Sons155)

8-10
EM 1110-2-1901

30 Sep 86

required. Well-graded materials are internally unstable and should not be used

as filters when Cu > 20.(l)

c. Discharge Requirements. Vertical (or inclined) and horizontal

drains must have sufficient discharge capacities to remove seepage quickly

without inducing high seepage forces or hydrostatic pressures (Cedergren

1977). When drains are designed and constructed with ample discharge capacity, the line of seepage will not rise above the drain zone. Since drains are

small compared to the overall dimensions of the earth dam, it is difficult to

construct accurate flow nets within the drains themselves. The total quantity

of seepage from all sources that must discharge through the drain should be

evaluated from a flow net analysis in which it is assumed that the drains have

an infinite permeability. Figure 8-9 shows an example of the design procedure

for inclined and horizontal drains to assure adequate drain capacity (Cedergren

1977). The probable rate of discharge through the dam and foundation is estimated from composite flow nets (see figures 4-13 and 4-14). For the example

shown in figure 8-9 , the seepage through the dam Q1 = 2 cu ft/day and the

seepage through the foundation Q2 = 10 cu ft/day. Therefore, the inclined

drain must be capable of discharging Q1 = 2 cu ft/day and the horizontal drain

must be capable to discharging Q1 + Q2 = 12 cu ft/day. These are discharge

rates per running foot of dam and drain. Assuming the inclined drain was

designed with a width of 12 ft to permit its placement with normal earth-moving

equipment, the cross-sectional area normal to the direction of flow within the

inclined drain Ac = 11 sq ft (see figure 8-9b) and its required minimum

permeability may be found from Darcy's law:

(8-2)

(1)

where Cu = coefficient of uniformity

= size of filter material at 60 percent passing

= size of filter material at 10 percent passing

8-11
EM 1110-2-1901

30 Sep 86

where

k = coefficient of permeability

Q = quantity of discharge

i = hydraulic gradient

A = cross-sectional area of flow

a. Cross section and flow net

b. Dimensions of inclined drain

c. Dimensions of horizontal drain

Figure 8-9. Example of design procedure for inclined and horizontal drains

to assure adequate drain capacity (courtesy of John Wiley and Sons

155 )

8-12
EM 1110-2-1901

30 Sep 86

Substituting for Q , 1 , and A

(8-3)

Every filter must be permeable enough to have a reasonable reserve for higher

than expected flows. The filter should have a minimum permeability after

placement and compaction of at least 20 times that calculated theoretically.

Therefore, the required permeability for the inclined drain is

(8-4)

Clean, washed concrete sand is usually about this permeable. As previously

stated,

ft/day.

the horizontal drain must be capable of discharging Q1 + Q2 = 12 cu

Since the drain is to be designed so that the line of seepage does

not rise above the drain zone, the allowable maximum head in the horizontal

drain can be no greater than its height. The required minimum permeability

from Darcy's law is

(8-5)

Substituting Ab = hb (width is one running foot of dam and drain)

8-13
EM 1110-2-1901

30 Sep 86

(8-6)

To design the horizontal drain, select a drain height and calculate the

required minimum permeability. Apply a factor of safety of 20 to the calculated permeability and select a drain material from available aggregates.

Select a drain height of 4 ft.

The required permeability for design is

This permeability could be obtained by screened fine gravel (3/8-in. to 1/2-in.

size) which has a permeability of about 30,000 ft/day or 10.6 cm/sec

8-14
EM 1110-2-1901

30 Sep 86

(Cedergren 1977). Seepage in coarse aggregate is likely to be turbulent and a

reduction factor should be applied to the permeability. The hydraulic gradient

in the horizontal drain is

From figure 8-10, for screened fine gravel (3/8-in. to 1/2-in. size) with

1 = 0.007 the reduction factor for permeability is 0.9.

(8-7)

(8-8)

The permeability of the screened fine gravel (3/8-in. to 1/2-in. size) reduced

for turbulence is greater than the required permeability for design:

Therefore, it should be adequate when properly placed and compacted to conduct

seepage water through the horizontal drain. The screened fine gravel (3/8-in.

to 1/2-in. size) will be protected top and bottom with a 1-ft-thick clean

washed concrete sand filter. Since the seepage from the foundation must flow

across the fine filter to enter the coarse drainage layer, the fine filter must

be permeable enough to allow the water to enter the coarse drainage layer

freely under only a small hydraulic gradient (0.5 or less). Assume an average

hydraulic gradient of 0.5 across the fine filter layer and Q2 = 10 cu ft/day

for the amount of water that will enter the first (left) 200 ft of the drain.

From Darcy's law the required minimum permeability of the fine filter is (see

equation 8-2)

k = 0.1 ft/day

8-15
EM 1110-2-1901

30 Sep 86

Figure 8-10. Approximation for estimating reduction

in permeability of narrow size-range aggregate

caused by turbulent flow (courtesy of John Wiley

and Sons155)

Clean washed concrete sand with a permeability of 10 ft/day should allow

seepage from the foundation to enter the coarse drainage layer without

restriction. As stated previously, the inclined and horizontal drains used in

this example would have to meet the filter requirements (see Appendix D) in

addition to the discharge requirements.

d. Location and Geometry. Vertical (or inclined) drains are located

adjacent to and downstream of the core as shown in figure 8-2. The top of the

vertical (or inclined) drain should be above the phreatic surface for maximum

reservoir elevation to prevent seepage flow above the drain. In drawing the

flow net for the dam to use in selecting the height and location for the vertical or inclined drain, a conservative (high) value of anisotropy of permeability of the soil should be used in order to prevent the seepage from flowing over the top of the drain (see figure 8-11). If the dam is located where

earthquake effects are likely (see paragraph 8-6) , the vertical (or inclined)

drain should extend the full height of the dam. The width of the vertical (or

inclined) drain is controlled by the availability of materials and the discharge requirements of the drain. A vertical (or inclined) drain width of

6 ft is the practical minimum for earth-moving and compaction equipment (U. S.

Army Engineer District, Kansas City 1974 and U. S. Army Engineer District,

Philadelphia 1974). When filter or drain material is not available locally and

must be hauled to the site at a substantial cost, a narrow (3 ft or greater)

vertical drain may be constructed by excavating into the core material, backfilling, and compacting with vibratory equipment (U. S. Army Engineer District,

Mobile 1965, U. S. Army Engineer District, Tulsa 1974). The width of the vertical drain must be sufficient to satisfy the discharge requirements. Horizontal drains are located under the downstream section of the dam and convey

seepage from the vertical (or inclined) drain and underseepage from the

8-16
EM 1110-2-1901

30 Sep 86

CORRECT WAY INCORRECT WAY

Figure 8-11. Use of stringers or finger drains as an alternative

to a continuous horizontal drain (prepared by WES)

foundation to the toe of the dam. The thickness of the horizontal drain must

be sufficient to satisfy the discharge requirements. When filter or drain

material is not available locally and must be hauled to the site at substantial

cost, a thin (2 ft or greater) horizontal drain has been used (U. S. Army Engineer District, Tulsa 1975 and U. S. Army Engineer District, Louisville 1974).

Stringers or finger drains may be used as an alternative to a continuous horizontal drain, as shown in figure 8-11, when the drain material is costly. The

cross-sectional area of the stringer drains must be sufficient to satisfy the

discharge requirements. The stringer drain may be constructed either by

trenching into the embankment or foundation for narrow (6 ft) widths or by

placing the adjacent impervious fill and then the drain material for wider

(50 ft) widths (U. S. Army Engineer District, Kansas City 1974, 1978). In

either case, the side slopes of the stringer drains should be sloped instead of

8-17
EM 1110-2-1901

30 Sep 86

vertical (see figure 8-11) to avoid stress concentrations which could cause

vertical transverse cracks. The stringer drain material must be thoroughly

compacted (see paragraph 8-4c) to ensure that consolidation does not occur upon

saturation leaving an open seepage conduit in the top of the trench, bridged by

the overlying embankment, and susceptible to progressive erosion (Jansen 1980).

The downstream end of horizontal drains and stringer drains must be able to

discharge freely and must be protected against siltation and erosion. This may

be accomplished by providing a weighted filter (riprap overlying bedding material) or a toe drain as shown in figure 8-12 (U. S. Army Engineer District,

Mobile 1965 and U. S. Army Engineer District, Tulsa 1975). The toe drain has

the advantage of lower maintenance requirements and preventing the development

of localized wet areas at the surface along the downstream toe of the

embankment.

8-6. Seepage Control Against Earthquake Effects. For dams located where

earthquake effects are likely, there are several considerations which can lead

to increased seepage control and safety.- The core material should have a high

resistance to erosion (Arulanandan and Perry 1983). Relatively wide transition

and filter zones adjacent to the core and extending for the full height of the

dam can be used. Additional screening and compaction of outer zones or shells

will increase permeability and shear strength, respectively. Geometric considerations include using a vertical instead of inclined core, wider dam crest,

increased freeboard, and flatter embankment slopes, and flaring the embankment

at the abutments (Sherard 1966, 1967).

8-18
EM 1110-2-1901

30 Sep 86

a. Weighted filter (courtesy of U. S. Army

Engineer District, Mobile97)

b. Toe drain (courtesy of U. S. Army Engineer District, Tulsa 113)

Figure 8-12. Protection of downstream end of horizontal and

stringer drains

8-19
EM 1110-2-1901

30 Sep 86

CHAPTER 9

SEEPAGE CONTROL IN EARTH FOUNDATIONS

9-1. General. All dams on earth foundations are subject to underseepage.

Seepage control in earth foundations is necessary to prevent excessive uplift

pressures and piping through the foundation (seepage control in earth abutments is given in Chapter 10). The purpose of the project, i.e., long-term

storage, flood control, hydropower, etc., may impose limitations on the allowable quantity of seepage. Generally, siltation of the reservoir with time

will tend to diminish underseepage (U. S. Army Engineer Division, Ohio River

1945). Conversely, the use of some underseepage control methods such as relief

wells and toe drains may increase the quantity of underseepage (Sowers 1962).

9-2. Selection of Method for Seepage Control. The methods for control of

underseepage in dam foundations are horizontal drains, cutoffs (compacted backfill trenches, slurry walls, concrete walls, and steel sheetpiling (1)), upstream impervious blankets, downstream seepage berms, toe drains, and relief

wells. To select an underseepage control method for a particular dam and

foundation, the relative merits and efficiency of different methods should be

evaluated by means of flow nets or approximate methods as described in

Chapter 4 and Appendix B, respectively. As shown in table 9-1, the changes in

the quantity of underseepage, factor of safety against uplift, and uplift pressures at various locations should be determined for each particular dam and

foundation. Since the anisotropy ratio of the foundation has a significant

influence on the results of the underseepage analysis, this parameter should be

varied as appropriate to cover the possible range of

expected field conditions.

9-3. Horizontal Drains. As mentioned previously in Chapter 8, horizontal

drains are used to control seepage through the embankment and to prevent

excessive uplift pressures in the foundation. As shown in figure 9-1, the use

of the horizontal drain significantly reduces the uplift pressure in the foundation under the downstream portion of the dam. The computation of uplift

pressure was illustrated previously in figure 4-15. Figure 9-1 also shows

that the horizontal drain increases the quantity of seepage under the dam.

9-4. Cutoffs.

a. Complete Versus Partial Cutoff. When the dam foundation consists of

a relatively thick deposit of pervious alluvium, the designer must decide

whether to make a complete cutoff (compacted backfill trench, slurry trench,

or concrete wall) or allow a certain amount of underseepage to occur under

controlled conditions (partial cutoff , upstream impervious blanket, downstream

seepage berm, toe trench drain, or relief walls), In some cases, where the

alluvium is not very deep or the water is very valuable, it may be obvious

(1) Steel sheetpiling is not recommended to prevent underseepage but is used

to confine the foundation soil and prevent piping.

9-1
9-2

Table 9-1. Selection of Underseepage Control Method 

Method 

Horizontal Drain 

Complete Cutoff 

Partial Cutoff 

Upstream Impervious Blanket 

Downstream Seepage Berm 

Toe Drain 

Relief Wells 

Changes in 

Quantity of 

Under seepage 

F 

s 

i (a) 

c 

i 

e 

Uplift Pressure 

Under Dam Toe of Dam Downstre

r-------------------

1 Fill in table for each particular 

I dam and foundation. Vary the 

I permeability anisotropy of the 

I (K I foundation = 1, 10, 25, 100) as L 

___________________

(a) Factor of safety against uplift at downstream toe of dam given by the ratio of 

critical hydraulic gradient to the vertical component of the exit gradient. 

(prepared by WES) 
EM 1110-2-1901

30 Sep 86

Figure 9-1. Influence of horizontal drain on uplift pressure

(prepared by WES)

after relatively little study that a complete cutoff is justified. For

example, the hydropower requirements of the Clarence Cannon Dam, Missouri,

indicated that a complete cutoff was required to sustain power requirements

during periods of little or no rainfall (U. S. Army Engineer District,

St. Louis 1969). In many cases, where the cost of a complete cutoff is great

and where the amount of underseepage without a complete cutoff is problematical, the decision is not easy. Factors which govern the decision for the type

of underseepage control measure to be used are (Sherard 1968):

(1) Economic comparison of the value of the water or hydropower which

may be lost versus the cost of the complete cutoff.

9-3
EM 1110-2-1901

30 Sep 86

(2) The resistance of the foundation alluvium with respect to potential

progressive backward erosion of leaks or piping. If the foundation contains

layers of fine sand or cohesionless silt, and particularly if these soils are

exposed on the surface of the valley floor or walls, a complete cutoff is more

desirable than if the foundation is basically gravelly (or even coarse sand).

If a large leak develops in a relatively coarse alluvium, in all probability

it will be safe against progressive backward erosion, but even a small concentrated leak emerging below the dam in fine cohesionless soils can be

hazardous.

(3) If the tailwater conditions are such that ponds of water exist

downstream of the dam so that underseepage would emerge underwater and could

not be observed, it is desirable to be more conservative in evaluating the

need for a complete seepage cutoff.

(4) The amount of silt and clay sized particles in suspension in the

river water which contributes to siltation of the reservoir with time and

tends to diminish underseepage.

Theory and model tests indicate that it is necessary for a cutoff to penetrate

a homogeneous isotropic foundation at least 95 percent of the full depth before

there is any appreciable reduction in seepage beneath an earth embankment as

shown in figure 9-2 (Telling, Menzies, and Coulthord 1978; and Mansur and

Perret 1949). The effectiveness of the partial cutoff in reducing the quantity of underseepage decreases as the ratio of the width of the dam to the

depth of penetration of the cutoff increases (see figure 9-2). Partial cutoffs are effective only when they extend down into an intermediate stratum of

lower permeability. This stratum must be continuous across the valley foundation to ensure that three-dimensional seepage around a discontinuous stratum

does not negate the effectiveness of the partial cutoff.

b. Efficiency of Cutoffs. The effectiveness of the cutoff is assessed

either in terms of the flow efficiency (Casagrande 1961)

(9-1)

where

E q = flow efficiency of cutoff

Qo = rate of underseepage without cutoff

Q = rate of underseepage with cutoff

or head efficiency (Lane and Wohlt 1961)

(9-2)

9-4
EM 1110-2-1901

30 Sep 86

where

EH = head efficiency of cutoff

h = head loss between points immediately upstream and downstream of the

cutoff wall at its junction with the base of the dam

H = head loss across the dam

The head efficiency is more widely used because the field performance may be

established from piezometric data taken during construction, before and during

initial filling of the reservoir, and subsequently as frequently as necessary

to determine changes that are occurring and to assess their implications with

respect to safety of the dam, as described in Chapter 13. The flow efficiency

may only be approximated since the rate of underseepage without the cutoff

cannot be directly established and since it is difficult to measure the rate

of underseepage with the cutoff because, except for special cases, only part

of the underseepage discharges at the ground surface immediately downstream of

the dam (Telling, Menzies, and Simons 1978a and Marsal and Resendiz 1971). The

flow efficiency of a compacted backfill partial cutoff in a foundation of

permeable soils of moderate thickness overlying an impervious rock is shown in

figure 9-3. This figure also illustrates the high seepage gradients that occur

along the base of the cutoff and on its downstream face in both the foundation

and embankment zones. Suitable filters must be provided to prevent piping of

soil at faces A-B-C in figure 9-3a and 9-3b (Cedergren 1977 and Klohn 1979).

As shown in figure 9-4, a partial cutoff in a homogeneous isotropic foundation

will lower the line of seepage in the downstream embankment somewhat but exit

gradients at the downstream toe (as reflected by the distance between the

equipotential lines) are reduced only slightly (Cedergren 1973). When the

pervious foundation is cut off by a compacted backfill or slurry trench, (1) the

rate of underseepage may be estimated by (Ambraseys 1963 and Marsal and

Resendiz 1971)

where

Qo

3

= rate of underseepage in m /set per running meter of dam

KO = permeability of the foundation in m/sec

(9-3)

(1) This approach neglects the contribution of the filter cake that forms on

the trench walls to the overall slurry trench permeability. When the

permeability of the backfill placed in the trench is high, the overall

slurry trench permeability will be controlled by the filter cake

(D'Appolonia 1980).

9-5
EM 1110-2-1901

30 Sep 86

H = head of water in the reservoir in m

B = width of the base of the dam in m

D = thickness of the foundation in m

k = permeability of the compacted backfill or slurry trench backfill in

m/sec

E = thickness of the cutoff in m

For a concrete wall or steel sheetpiling with defects (openings in the cutoff)

the rate of underseepage per unit length of cutoff is given by (Ambraseys 1963

and Marsal and Resendiz 1971)

(9-4)

where

W = total area of openings in m2

Figure 9-5 compares the rate of underseepage for an impervious upstream

blanket, compacted backfill trench or slurry trench, and concrete wall or

steel sheetpiling with defects. As shown in figure 9-5, the rate of

underseepage loss is the same for an impervious upstream blanket as for a

compacted backfill trench or slurry trench provided B' =

If K is relatively high, assuming gives B' = 49 E . Such computations allow preliminary cost estimates to be made to determine whether an

impervious upstream blanket is preferable over a compacted backfill trench or

slurry trench. Figure 9-6 can be used to determine the relative magnitudes of

the length of the impervious upstream blanket, the thickness of the compacted

backfill trench or slurry trench, or the area of the defects (openings) in the

concrete wall or steel sheetpiling that would result in the same rate of

underseepage for a given dam.

c. Compacted Backfill Trench. The most positive method for control of

underseepage consists of excavating a trench beneath the impervious zone of the

embankment through pervious foundation strata and backfilling it with compacted

impervious material. The compacted backfill trench is the only method for

control of underseepage which provides a full-scale exploration trench that

allows the designer to see the actual natural conditions and to adjust the

design accordingly, permits treatment of exposed bedrock as necessary, provides

access for installation of filters to control seepage and prevent piping of

soil at interfaces, and allows high quality backfilling operations to be carried out (U. S. Army Engineer District, St. Louis 1969 and Cedergren 1977).

9-6
9-7

L 

20 

D 0 J:o 

1-x 

n..o 

0"'0 w, 40 

lL.. 0 .. 0 

1-w 

zlucr 

a:fww 

CLZ 

w 

Q.. 

20 40 60 80 

PERCENT OF TOTAL SEEPAGE 

Figure 9-2. Effect of depth of penetration of partial cutoff on seepage reducti

homogeneous isotropic foundation (prepared by WES) 
EM 1110-2-1901

30 Sep 86

a. Partial cutoff

b. Complete cutoff

c. Relationship between quantity

of seepage and depth of

penetration of partial cutoff

Figure 9-3. Efficiency of a compacted backfill trench partial cutoff

in reducing the quantity of underseepage (courtesy of John Wiley

and Sons155)

9-8
EM 1110-2-1901

30 Sep 86

a. Flow net for no cutoff

b. Flow net for partial cutoff

c. Position of line of seepage for various values

of penetration

Figure 9-4. Effect of depth of penetration of partial cutoff on

the height of the line of seepage in the downstream embankment

and exit gradient at the toe for a homogeneous isotropic

foundation (courtesy of John Wiley and Sons

154

)

9-9
EM 1110-2-1901

30 Sep 86

Impervious upstream Compacted back Concrete wall or

blanket fill or slurry steel sheetpiling

trench

Figure 9-5. Rate of underseepage loss for impervious

upstream blanket, compacted backfill trench or slurry

trench, and concrete wall or steel sheetpiling with

defects (courtesy of American Society of Civil

218 Engineers )

Material and compaction requirements are the same as those for the impervious

section of the dam (EM 1110-2-1911). When constructing a complete cutoff (see

para 9-4a), the trench must fully penetrate the pervious foundation and be

carried a short distance into unweathered and relatively impermeable foundation

soil or rock. To ensure an adequate seepage cutoff, the base width should be

at least one-fourth the maximum difference between the reservoir and tailwater

elevations but not less than 20 ft, and should be wider if the foundation

material under the cutoff is considered marginal in respect to imperviousness.

As previously mentioned (see para 9-4b), high seepage gradients occur along the

base of the cutoff and on its downstream face in both the foundation and

embankment zones. Suitable filters must be provided (see Appendix D for design

of filters) to prevent piping of soil at these interfaces. The trench

9-10
EM 1110-2-1901

30 Sep 86

Figure 9-6. Relationships among the length of the

impervious upstream blanket, the thickness of the

compacted backfill trench or slurry trench, or the

area of defects in the concrete wall or steel sheetpiling, for a given rate of underseepage loss

(courtesy of American Society of Civil Engineers218 )

excavation must be kept dry to permit proper placement and compaction of the

impervious backfill. Dewatering systems of wellpoints or deep wells are

generally required during excavation and backfill operations when below

groundwater levels (TM 5-818-5). Because construction of an open cutoff trench

with dewatering is a costly procedure , the trend has been toward use of the

slurry trench method of construction (EM 1110-2-2300 and Cedergren 1977).

d. Slurry Trench.

(1) Introduction. When the cost of dewatering and/or the depth of the

pervious foundation render the compacted backfill trench too costly and/or

impractical, the slurry trench cutoff may be a viable method for control of

9-11
EM 1110-2-1901

30 Sep 86

underseepage. Using this method, a trench is excavated through the pervious

foundation using a sodium bentonite clay (or Attapulgite clay in saline water)

and water slurry to support the sides. The slurry-filled trench is backfilled

by displacing the slurry with a backfill material that contains enough fines

(material passing the No. 200 sieve) to make the cutoff relatively impervious

but sufficient coarse particles to minimize settlement of the trench forming a

soil-bentonite cutoff (sometimes called American method). Alternatively,

cement may be introduced into the slurry-filled trench which is left to set or

harden forming a cement-bentonite cutoff (sometimes called a grouted diaphragm

wall or Coulis wall or European method). The slurry trench cutoff is not

recommended when boulders, talus blocks on buried slopes, or open jointed rock

exist in the foundation due to difficulties in excavating through the rock and

slurry loss through the open joints. Where a slurry trench is relied upon for

seepage control, the initial filling of the reservoir must be controlled and

piezometers located both upstream and downstream of the cutoff must be read to

determine if the slurry trench is performing as planned. If the cutoff is

ineffective, remedial seepage control measures (see Chapter 12) must be

installed prior to further raising of the reservoir pool (KM 1110-2-2300).

(a) History of Use. The first use of the slurry trench method of construction was by the U. S. Army Engineer District, Memphis, in September 1945,

to form a partial cutoff along the Mississippi River levee on the Arkansas

side of the river just below Memphis, Tennessee (Clay 1976 and Kramer 1946).

The idea for the project probably evolved from the use at that time of puddle

clay trench cutoffs combined with the use of drilling mud for advancing

borings. A paddle wheel mixing device was constructed for making slurry from

native clays. Trenches were dug to a 20-ft depth using a trenching machine and

to a 35-ft depth using a dragline with a 100-ft boom and 2-cu-yd bucket.

Backfill was mixed in windrows at the site from hauled-in clay gravel and

native materials and pushed into the trench by a bulldozer when the length of

the trench was equal to about twice the trench depth. BG Hans Kramer foresaw

the use of the slurry trench method for the construction of cutoffs for earth

dams. It is amazing that after 38 years, the technique is still about the same

as it was when first developed by the Memphis District. A soil-bentonite

cutoff was constructed under the Kennewick Levee adjacent to the Columbia River

as part of the McNary Dam Project in Washington by the Walla Walla District in

1952 (Jones 1961). The first application of a soil-bentonite slurry trench

cutoff for control of underseepage at a major earth dam was at Wanapum Dam on

the Columbia River in Washington in 1959 (La Russo 1963). Subsequently, soilbentonite cutoffs have been used for control of underseepage at a number of

dams as shown in table 9-2. The cement-bentonite slurry trench cutoff was

first used to tie into the abutment zones at the Razaza Dam on the Euphrates

River in Iraq in 1969 (Soletanche 1969). Subsequently, cement-bentonite cutoffs were installed as remedial seepage control measures through the embankment and foundation of four existing dams in Mexico from 1970 to 1972

(Soletanche 1970, 1971, 1971-1972, 1972). As shown in table 2, the first

cement-bentonite cutoff in the United States was constructed at the Tilden

Tailings Project to store tailings from the Tilden Mine in Michigan in 1976

(Meier and Rettberg 1978). The first cement-bentonite cutoff constructed at a

dam on a river retaining a reservoir in the United States was completed in

1978 at the Elgo Dam (formerly the San Carlos Dam) in Arizona (Anonymous 1978

and Miller and Salzman 1980).

9-12
EM 1110-2-1901

30 Sep 86

9-13

Table ?-2. Comparison of Slurry Trench Cutoffs 

Max. Hal<. 

Differential 

!late Head Width De~th 

Pro1ect Location Owner Constructed Foundation Uaterial ft __!!._ __!!._ Location ~ Reference 

Soil-Bentonite Slurrv Trench 

Kennewick Levee, Columbia River .. Corps of Engineers 1952 Sandy or silty gravel with 15 22 Center of 2. 5 Jones 1961 

t-tcNa.ry Dam Wash. z:ones of open gravel dam 

Wou>aj>ua n- Col.-hi.a Uve.r. Pllfllie UUlUy 1962 S<md, g1"3"ftls ...,d. g,;ave!.ly 88 10 80 Center o£ 8.8 L.a Russo 1963 

wasn. District 2 .. Grant sands underlain by open da10 

County, Wasb. wrk gravels 

Wells Dam Columbia River, l'ublic Utility 1964 Pervious gravels 70 80 Center of 8.8 Jones 1967 

Wash. District 1. dam 

Douglass County, 

Wasb. 

Yards Creek Hew Jersey Public Service 1964 Sands~ gravels, cobbles, 55 8 40 Center of 6.9 Jones 1967 

Lo""r Reservoir Electricity and and boulders daa 

Gas 

Comanche Dam - Moke1UII!IIIe East Bay 1966 Opper stratum of clayey 45 95 Upstream 5.6 Anton and 

Dike 2 River, CaUf. )!unicipal District silts, silts, and clayey of toe of Dayton 1972 

sands .. Lower stratum of da.. 

sand over zone of gravel 

\lest Point Dat'l Chattabocchie Corp~ of Eng1neers 1966 Upper stratum of alluvial 61 60 Upstream 12.2 u.s. Army 

River, Ca. soil~ alternating layers toe of dam Engr~ Dist, 

.and Ala.,. of clay. si~t, sanO, a.ncl Savannah 

gfa'Vel. Lower stratum. of 1968, 1979 

residual soil, brown 

oHty sand 

Saylorville Des: !ok>ines Corps of Engineers 1969 Surface zone of sandy clay. 93 65 Upstrf'am 11.6 Harza 1965, 

llaa River, Iowa Lower st.rattm of sand and toe of dam u.s. Army 

gravel Engr. Dist. 

Rock Island 

1978 

Mill Site ferron Creek. Soil Conservation 1969 Sandy gravel 73 68 Upstrf!am 9.1 H.anoon 1972 

llaa Utab Service toe o:!. dam 

Plum Creek Plum Creek., Soil Conservation 1973 Sands, gravelly sands. 54 40 Ce.ntet:' of 10.8 Knabach and 

llaa Wis. Service silty gravels, silty sands dam Dingle 1914 

Upper Big Upper Big Soil Cortservet ion 1978 Sands and gravels 62 40 Center of 15.5 Bloom, Dynes, 

&lue Daa Blue R.iver, Service dam Glol!sett 

Ind. 1979 

Addicks lla,.(a) Buffalo Bayou, Co-rps of Engineers 1979 Silty aands 30 70 Varies 10.0 u.s. Anny 

Tex~ Engr .. Dist, 

Barker Dall(a) Buffalo Bayou, Corps of Engineers 1979 Sandy clay, clayey sand, 24 55 Cenr:er of 8.0 Galveston 

Tex .. ailty sand 1983 (sallie 

for Barker Da11) 

Celaent-Beatonite Slurrl Trench 

Tilden Tilden !line, Cleveland-Cliffs 1976 Sand interspersed witn gravel 100(b) 80 Upstream 51).0 Meier and 

Tailings Mieb. Iron Co11pany toe of dam ll.ettberg 

1918 

Elgo Dam San Carlos Sat'l Carlos Apac.he 1978 Sands and gravels 66 68 Center of 22.0 tliller and 

(formerly lU.ver, Ari•- Tribe dam Salzman 1980 

San Carlos 

Diu&) 

(a) Slurry trench c.ucof[ ins called aa reaedial seepage control for exlatina da11 (aee Chapter 12). 

(b) Planrted maximum differential head wben ta1.11ng;a dam is at final height (45 ft in February 1983}. 
EM 1110-2-1901

30 Sep 86

(b) Patents. The soil-bentonite slurry trench cutoff was covered by

United States Patent No. 2,757,514 dated August 7, 1956, "Method of Forming an

Impermeable Wall in the Terrain," in the name of Harold T. Wyatt. This patent

expired in 1973. The cement-bentonite slurry trench cutoff is covered by

United States Patent No. 3,759,044 dated September 18, 1973, "Method of Earth

Wall Construction Using Cementitious Bentonite Mud," in the name of Claude

Caron and Jean Hurtado, both of France, assignor to Soletanche, Paris, France.

(c) Comparison of Soil-Bentonite and Cement-Bentonite Slurry Trench

Cutoffs. A comparison of soil-bentonite and cement-bentonite slurry trench

cutoffs is given in table 9-3. The soil-bentonite slurry trench cutoff is

generally the most economical if the cost of backfill is not prohibitive. For

deep cutoffs where the foundation is prone to failure during excavation, the

cement-bentonite slurry trench cutoff is more applicable.

(d) Location of Cutoff. Normally, the slurry trench should be located

under or near the upstream toe of the dam (EM 1110-2-2300). An upstream

location provides access for future treatment provided the reservoir could be

drawn down and facilitates stage construction by permitting placement of a

downstream shell followed by an upstream core tied into the slurry trench. For

stability analysis, a soil-bentonite slurry trench cutoff should be considered

to have zero shear strength and exert only a hydrostatic force to resist

failure of the embankment (U. S. Army Engineer District, Savannah 1968). If

the slurry trench is located under a central core, consolidation of the slurry

trench backfill combined with arching of the core material immediately above

the slurry trench may result in the opening of a cavity under the dam with

possible leakage along the contact. If a central location for the slurry

trench is dictated by other factors, some possible benefits are obtained by

flaring the top of the trench to provide a transition between the cutoff and

the core. Also, the slurry trench can be constructed and allowed to settle

before placement of the embankment (Jones 1967 and Jansen 1968). When the

groundwater table is located some distance beneath the ground surface, it is

usually more economical to excavate a conventional open trench with stable side

slopes with the trench bottom a few feet above the highest level of ground

water expected during the construction period, as was done at West Point Dam,

Alabama and Georgia (U. S. Army Engineer District, Savannah 1968). The bottom

of the open trench provides a working level from which the slurry trench may be

constructed. Also, this prevents the problem of significant amounts of slurry

being lost into the excavated trench above the ground-water table. If the

ground-water table is located near the ground surface, compacted impervious

fill should be placed in order to raise the level of the slurry trench to

maintain the level of slurry in the trench a sufficient distance above the

ground-water level (Jones 1967).

(e) Stability of the Trench. In cohesionless soils the penetration of

the slurry into the wall of the slurry trench excavation forms a relatively

impervious filter cake on which the hydrostatic pressure of the slurry can

act. The depth of penetration ranges from 1 to 3 in. in sand, 3 to 6 in. in

sand and gravel, and up to 12 in. in gravel, depending on the gradation. The

main stabilizing force supporting the slurry trench excavation is the hydrostatic pressure exerted on the trench walls. For a slurry trench excavated in

a homogeneous clay, remaining open only for a few days to permit placement of

9-14
9-15

Table 9-3. Comparison of Soil-Bentonite and Cement-Bentonite Slurry Trench Cutoffs(a) 

Item 

1. Excavation 

2. Slurry 

' 3. Backfill 

4. Properties of completed cutoff: 

a. Permeability 

b. Strength 

c. Consolidation 

5. Susceptible to attack by 

sulphates or other chemicals 

in groundwater 

6. Relative cost 

7. Patent applicable 

Soil Bentonite Slurry Trench Cutoff 

Long slope of backfill requires trenching continuously in one direction. 

Can accommodate interruptions in construction. 

Difficult to work with coarse gravels, with 

backhoe and/or dragline, which settle out and 

accumulate on the trench bottom reducing the 

certainty of a tight seal. 

Wider trench required to prevent segregation during backfilling (> 3 ft) and prevent piping 

failure of the trench backfill into the 

adjacent soil downstream of the cutoff (1 ft 

width for each 10 ft of differential head) 

Mixture of bentonite and water used to support 

excavation during trenching. Slurry displaced by 

backfill is desanded and reused. Upon completion 

of trench, unused slurry must be disposed of in 

an environmentally acceptable fashion. 

Mixture of slurry plus excavated material from 

trench and/or imported select backfill materials 

= 10-7 em/sec 1 percent bentonite) 

Little field data available - assumed zero for 

design purposes. 

Some consolidation with time. 

No 

Generally lower if cost of backfill is not 

prohibitive (see 3) 

No (expired 1973) 

Cement-Bentonite Slurr

Construction sequence is more 

constraints. 

Excavation for each panel sho

rupted so each panel is comp

begins to set. 

Easier to remove coarse grave

mounted on a rigid Kelly bar, 

bottom. Better suited for exprone to failure. 

Narrower trench (2 - 3 ft) ma

Mixture of cement, bentonite, 

support foe panel 

permanent backfill. No dispo

slurry required. 

None (see 2). Therefore•not 

bilityor quality of soil for 

.suitable for work in confined 

= 10-6 em/sec 

15 - 20 lbs/sq in. unconfined 

Will support construction loa

structures ftfter several week

No significant consolidation 

Yes - cement may be. 

Generally higher due to cost 

competitive as depth of trenc

narrower trench width require

Yes (United States Patent No. 

September 18, 1973) 

(a) f E i · c · I t t · 1 Inc . 132 • 249 , can Soc1· ety of C1

Courtesy o ng neer1ng onstruct1on n erna 

lana , 

- - • 1 • • • 221 
EM 1110-2-1901

30 Sep 86

backfill material, the factor of safety against instability is (Nash and Jones

1963)

(9-5)

where

F = factor of safety

Cu = undrained cohesion

H = depth of the trench

= unit weight of the soil

= unit weight of the slurry

For a slurry trench excavated in dry cohesionless soil (Nash and Jones 1963)

where angle of internal friction.

For a slurry trench excavated in a saturated cohesionless soil with the

ground-water table and slurry level in the excavation both at the ground

surface (Nash and Jones 1963)

where

= effective unit weight of the soil

= effective unit weight of the slurry

= effective angle of internal friction

(9-6)

(9-7)

For arbitrary levels of ground water and slurry in cohesionless soil, as shown

in figure 9-7a, a slightly conservative (neglects arching effect of short

9-16
EM 1110-2-1901

30 Sep 86

trenches and stabilization of the soil adjacent to the trench face due to

slurry penetration and gelation) estimate of the slurry density required to

ensure stability of the trench is (Morgenstern and Amir-Tahmasseb 1965)

(9-8)

where

n = defined in figure 9-7a

= unit weight of the slurry

= unit weight of water

= unit weight of the soil

= angle of inclination of the wedge of soil at the point of slipping,

in practice assumed to be equal to 45" +

effective angle of internal friction

m = defined in figure 9-7a

Equation 9-6 may be solved by use of the nomograph shown in figure 9-7b

(Duguid et al. 1971).

(2) Slurry. The slurry has three basic functions in slurry trench

construction (Ryan 1977):

• To hold the trench open and maintain a stable excavation.

• To be fluid enough to permit passage of the excavating equipment and to allow placement of the backfill (for the cement-bentonite slurry

trench, there is no backfill).

• To form a filter cake to enhance the low permeability of the

completed trench.

(a) Materials. As a general rule sodium montmorillonite in powder form

(Wyoming-type bentonite) is used for slurry trench construction. However,

when salt water is present Attapulgite clay is used to avoid flocculation

(Spooner et al. 1982). Specifications for both bentonite and Attapulgite are

given by the American Petroleum Institute (American Petroleum Institute 1981).

Each shipment of bentonite or Attapulgite should be checked for compliance with

the specifications. At Saylorville Dam, Iowa, changes in slurry properties

were traced to lower quality bentonite which was mined from different beds

(U. S. Army Engineer District, Rock Island 19788). No chemically treated

9-17
EM 1110-2-1901

30 Sep 86

a. Slurry trench typical section

b. Nomograph for slurry

trench stability

Figure 9-7. Determination of slurry

trench stability in cohesionless

soil (courtesy of National Research

Council of Canada 168)

9-18
EM 1110-2-1901

30 Sep 86

bentonite should be used for slurry trench construction. The pH of the water

used for mixing with the bentonite should equal 7.0 ± 1.0. Water hardness

should not exceed 50 ppm (parts per million). Total dissolved solids should

not exceed 500 ppm. The amount of oil, organics, or other deleterious substances should be limited to no more than 50 ppm each (Stanley Consultants,

Inc., and Woodward-Clyde Consultants 1977). If the use of poor quality water

cannot be avoided, it will require more bentonite and longer mixing times to

achieve the desired properties.

(b) Mixing. The methods used to prepare the hentonite slurry vary with

project size and layout. Always add the bentonite to the water, never the

water to the bentonite. For small jobs the batch system is used where

specific quantities of water and bentonite are placed in a tank and mixed at

high speeds with a circulationpump or paddle mixer and the slurry is discharged into the trench. Mixing is usually complete in a matter of minutes

for the 2- to 5-cu-yd batch produced by this method. The most commonly used

method is the flash or Venturi mixer and circulation ponds which is well

adapted for bulk handling of large slurry volumes. A flash mixer introduces

dry bentonite into a turbulent water jet which discharges into a low speed

circulation pond. When Marsh Funnel viscosity readings stabilize, the slurry

is stored in a second pond prior to using the trench (Spooner et al. 1982 and

D'Appolonia 1980).

(c) Properties. Tests of bentonite quality must be conducted for each

rail car or truck load delivered. The minimum acceptable viscosity of a slurry

made with the bentonite is 40 seconds Marsh funnel viscosity at 65° F. The

fresh slurry shall have a minimum Marsh funnel viscosity of 40 seconds at 65° F

and a pH of from 7 to 10, a bentonite content of from 3 to 7 percent by dry

weight (depending on the grade of bentonite), a unit weight of from 1.0 to

1.04 g/cm3 (about 65 lb/ft3), and the filtrate or water loss shall not be

greater than 20 at 100 lb/in.2 x cm

3

in 30 minutes (Spooner et al. 1982 and

U. S. Army Engineer District, Savannah 1968). The slurry in the trench should

be sampled at least twice daily with samples taken from the top of the trench

and at 10-ft vertical, 50-ft horizontal intervals along the trench center line.

During all stages of construction the minimum acceptable viscosity of the

slurry shall be 40 seconds Marsh funnel viscosity at 65° F. The minimum

in-trench slurry unit weight is based upon trench stability considerations (see

Equation 9-8 and Figure 9-7). The maximum in-trench slurry density is 85/ft3

to avoid buildup of sediment beyond the slurry capacity to hold it in suspension in the trench during excavation (Clough 1978).

(d) Quality Control Testing. In order to mix and maintain a proper

slurry to hold the trench open during excavation and form a filter cake for

the soil-bentonite slurry trench, quality control testing must be performed.

The property, frequency, standard (if any), and specified value for slurries

and their components are given in table 9-4. The quality of the mixing water

used can influence the slurry trench characteristics. If the specific values

for mixing water quality are not met, the bentonite will flocculate and settle

out and not form the filter cake on the sides of the trench. Poor quality

mixing water will increase the set time for cement-bentonite slurry trench

cutoffs. The bentonite is tested to be sure it will have the minimum viscosity required to keep the soil in suspension. The slurry is tested both after

9-19
9-20

Table 9-4. Summary of Quality Control Tests for Slurry Trench Cutoff 

Category or llaterial 

Mixing Water 

Bentonite 

Bentonite slurry (after 

mixing) 

Bentonite slurry (in trench) 

Cement 

Cement-bentonite slurry 

(after mixing) 

Property 

pH 

Hardness 

Total dissolved solids 

Oil, organics, etc. 

Viscosity Viscosity 

pH 

Bentonite content 

Unit weight 

Filtrate or water loss 

Viscosity 

Unit weight 

Slump 

Viscosity 

pH 

Bentonite content 

Unit weight 

Filtrate or water loss 

Cement/water ratio 

(a) American Petroleum Institute specification. 

Frequency 

Once per month 

Once per month 

Once per month 

Once per month 

Each railroad car or truck load 

Twice per day Twice per day 

Twice per day 

Twice per day Twice per day 

Twice per day 

Twice per day 

Twice per day Twice per day 

Twice per day 

Twice per day Twice per day 

Twice per day Twice per day 

Standard 

API RP 13B(a) 

API RP 13B API RP 13B API RP 13B 

API RP 13A API RP 13B API RP 13A 

None(b) 

API RP 13B API RP 13B API RP 13B API RP 13B ASTM C-143 (d) API RP 13B API RP 13A 

None 

API RP 13B API RP 13B 

None 

(b) Can be checked by evaporating the water from a known volume of slurry and weighing the remaining solids 

(c) Minimum in trench slurry unit weight is based upon trench stability considerations. 

(d) American Society for Testing and Materials Standard. 

7.0 1

2 50 pp

2 500 p

< 50 pp

> 40 se

> 40 se

7 - 10 3 - 7 p

1.01 - 

> 20 cm

> 40 se

minimum

2 - 5 i

40-50 s

10 - 13 

4 - 7 p

1.03 - 

< 165 c

0.17 - 
EM 1110-2-1901

30 Sep 86

mixing and in the trench to determine that it is dense enough to stabilize the

trench, but not so dense as to cause the backfill to settle too loosely, and

that it has sufficient viscosity to maintain cuttings in suspension (Stanley

Consultants, Inc., and Woodward-Clyde Consultants 1976).

(3) Excavation, Mixing, and Backfilling.

(a) Excavation. The preferred method of trench excavation depends upon

the required depth of the slurry trench cutoff, the nature of the subsurface

materials, and access to the trench at the ground surface. It is important to

ensure that the equipment used can maintain a continuous excavation line to

the total depth required. At depths less than about 50 ft, backhoes are generally the most rapid and least costly excavation method. Modified backhoes

with an extended dipper stick, modified engine, and counter-weighted frame can

excavate to about 80 ft deep. Draglines with weighted (> 10,000 lb) buckets,

which have been used in the depth range 60 to 80 ft, have been replaced by more

efficient extended backhoes. The clamshell bucket can excavate to depths in

excess of 150 ft. The clamshell may be mechanically operated attached to a

crane or hydraulically operated attached to a Kelly bar. On larger jobs, the

backhoe may be used to excavate the first 50 ft followed by a clamshell bucket

to excavate the primary and secondary panels to the impervious zone. Regardless of the equipment used, it should be capable of excavating a trench of the

desired width in a single pass in order to obtain a fairly consistent trench

width. The bucket used should be nonperforated to allow retention and removal

of sand particles from the trench. The continuity of the trench is tested by

passing the bucket or clamshell of the excavating tool vertically and horizontally along each segment of the trench before it is backfilled. Whatever

excavation method is used, it is important that good communications are maintained with the operator of the excavation equipment since abnormalities in

the trench excavation are usually noticed first by the equipment operator

(D'Appolonia 1980; Spooner et al. 1982; Bloom, Dynes, and Glossett 1979; Case

International Company 1982; and Winter 1978). Soil-bentonite slurry trench

cutoffs are excavated in a continuous trench as shown in figure 9-8a, while

cement-bentonite slurry trench cutoffs are excavated in a continuous trench or

in short sections or panels as shown in figure 9-8b. The cement-bentonite

slurry begins to harden within 2 to 3 hours after mixing. Alternate panels

are excavated under a cement-bentonite slurry and then allowed to partially

set. Intervening panels are excavated also under a cement-bentonite slurry

and a portion of the initial panel ends are removed to ensure continuity

between adjacent panels. Construction delays can cause problems in setup of

cement-bentonite slurry trench cutoffs because continued agitation of the

cement-bentonite slurry (more than 24 hours) reduces the ability of the cement

to set (Spooner et al. 1982).

(b) Bottom Treatment. The aquiclude used for the slurry wall foundations should be continuous, and relatively free of fractures and other pervious

zones. The cutoff wall should extend a minimum of 2 ft into clay (or 1 ft into

rock) to prevent weathered zones, desiccation cracks, or other geological

features from permitting seepage under the cutoff (Spooner 1982). As the

trench is excavated, heavier soil particles such as sand and gravel fall to the

bottom of the trench. The amount of sand accumulation on the trench bottom

depends upon the coarseness of the strata being excavated as well as the

9-21
EM 1110-2-1901

30 Sep- 86

a. Soil bentonite cutoff

b. Cement bentonite cutoff

Figure 9-8. Construction procedure for soil-bentonite

and cement-bentonite cutoffs (courtesy of American

Society of Civil Engineers222 )

excavation technique used. Although this sand layer may not have a direct

effect on trench stability, it may adversely affect the permeability of the

slurry trench cutoff wall (Spooner 1982). An air lift pump should be used to

remove the sand and gravel particles from the trench bottom prior to backfilling. When the slurry trench is keyed into a soil aquiclude after the trench

bottom has been cleaned thoroughly, a minimum of one split-spoon sample shall

be taken every 50 ft along the length of the trench to determine if additional

excavation is required (Winter 1978).

(c) Backfill Mixing and Placement. A minimum of one day is required

between trench excavation and backfilling in order to develop a low permeability filter cake on the trench walls (D'Appolonia 1980). Stockpiled material

from the trench excavation and/or material from borrow areas are mixed and

blended by windrowing, disc harrowing, bulldozing, or by blading to remove

lumps of clay, sand, or gravel. The backfill is then sluiced with slurry

(mixing with water shall not be permitted) and just prior to placement has a

consistency of a wet concrete with a slump of 5 in. ± 1 in. tested in

9-22
EM 1110-2-1901

30 Sep 86

accordance with ASTM C-143 (1) (Winter 1978 and Ryan 1976). The backfill is

placed continuously from the beginning of the trench in the direction of the

excavation to the end of the trench. Free dropping of the backfill material

through the slurry would produce segregation and is not allowed. Depending on

the steepness of the excavated slope, it may be necessary to lower the initial

backfill to the bottom of the trench with a crane and clamshell bucket until a

slope at the angle of repose of the backfill has been formed from the bottom of

the trench to the top of the excavation. The toe of the backfill slope is kept

to within 50 to 150 ft of the leading edge of the excavation to minimize the

open length of the slurry-supported trench while allowing enough space behind

the excavation for cleaning the trench bottom. Additional backfill is placed

by a bulldozer in such a manner that the backfill enters the trench and slides

progressively down the slope of the previously placed backfill and produces a

slope ranging from 1V on 5H to 1V on 10H. The slope of the backfill shall be

measured with soundings starting at the toe of the backfill in the bottom of

the trench and progressing up the backfill slope at 25-ft horizontal intervals.

A set of soundings shall be made at least for every 25 ft horizontal advancement of backfill placement. Once the natural slope of the backfill is established during initial placement of the backfill, the slope should remain nearly

the same. If the slope, or a portion of the slope, suddenly gets steeper, it

could be an indication that sediment is being trapped or that the backfill has

a pocket of relatively clean material (slurry not mixed in properly or was

washed out). If the slope suddenly gets flatter, it could indicate that a

pocket of slurry was trapped in the backfill or that the backfill does not

contain sufficient sand or coarser material (Stanley Consultants, Inc., and

Woodward-Clyde Consultants 1976; Winter 1978; and Ryan 1976).

(d) Temperature During Construction. The mixing and placing of backfill

shall be limited to days when the air temperature is not less than 20" F. Even

though the surface of the slurry trench freezes overnight, there will be no

difficulty breaking through the surface ice and continuing excavation during

the day. Frozen backfill or pieces of ice must never be placed in the trench

(U. S. Army Engineer District, Rock Island 1978a and Jones 1967).

(e) Protection of Top of Trench. The top of the completed slurry

trench cutoff should be immediately protected with a temporary 2- to 3-ftthick blanket of moist impervious fill material to prevent drying of the

backfill and formation of shrinkage cracks along which paths of seepage could

easily develop. The layer is temporary and is removed once the embankment

construction is started (Jones 1967; Stanley Consultants, Inc., and WoodwardClyde Consultants 1977).

(4) Soil-Bentonite Slurry Trench Cutoff.

(1) American Society for Testing and Materials standard. If a desirable backfilled slope (1V on 5H to 1V on 10H) cannot be maintained in the trench

with a 5 in. ± 1 in. slump, the slump may be altered to meet construction

conditions. Such was the case at the soil-bentonite slurry trench cutoff

constructed at W. G. Huxtable Pumping Plant, Marianna, Arkansas (U. S.

Army Engineer District, Memphis 1978).

9-23
EM 1110-2-1901

30 Sep 86

(a) Design Considerations. The primary design parameters are blowout

requirements, permeability, strength, and compressibility. The backfill material must not blow out into the surrounding pervious foundation under the

maximum differential hydraulic head that will act on the slurry trench. The

permeability is usually sufficiently low (-10-7 cm/sec for > 1 percent bentonite) to reduce the seepage through the slurry trench cutoff to an acceptable

value. Under most conditions, the only strength requirement for the slurry

trench cutoff is to approximate the strength of the surrounding ground. The

compressibility of the slurry trench cutoff, once consolidated under its own

weight (usually within 6 months after placement), should be compatible with the

compressibility of the surrounding ground to minimize differential movement of

the dam and resultant stress concentrations in the embankment or its foundation

(Ryan 1976 and Xanthakos 1979).

(b) Blowout Requirements. Once the slurry trench is installed, the dam

has been constructed, and the reservoir filled, there is a substantial differential head acting on the slurry trench (see table 9-2 for typical values).

Depending upon the characteristics of the backfill material and pervious foundation, the hydraulic gradient acting across the slurry trench may be sufficient to cause blowout or piping of backfill material into the surrounding pervious foundation. This is especially critical when the foundation contains

openwork gravel where the piping process could result in the formation of

channels and cavities that may breach the slurry wall. Based upon laboratory

tests conducted on widely graded gravel containing no sand, the blowout gradient ranges from 25 to 35, depending on the properties of the backfill material (La Russo 1963 and Nash 1976). The factor of safety against blowout is

(9-9)

where

F = factor of safety against blowout

i

allowable

= allowable hydraulic gradient from laboratory blowout tests

i

actual = actual hydraulic gradient existing on slurry trench

Substituting for the actual hydraulic gradient

(9-10)

where

= maximum differential hydraulic head acting on the slurry trench

w = slurry trench width

9-24
EM 1110-2-1901

30 Sep 86

and using a factor of safety of 3 and an allowable hydraulic gradient of 30 in

equation 9-9 gives

(9-11)

If the pervious foundation contains openwork gravel, the width of soilbentonite slurry trench required to prevent blowout failure may be estimated

from equation 9-11. Further refinements on the trench width would require conducting laboratory blowout tests (as described by Xanthakos 1979).

(c) Permeability. For design purposes the permeability of the soilbentonite slurry trench cutoff is based on the backfill material only

(Xanthakos 1979). The permeability of the slurry trench is a function of both

the filter cake that forms on the trench walls and the backfill material. The

contribution of the filter cake and the backfill depends on the relative

permeability and thickness of the two materials. The horizontal permeability

of the soil-bentonite slurry trench is (D'Appolonia 1980)

(9-12)

where

k = permeability of slurry trench

tb = backfill thickness

kb = backfill permeability

t = filter cake thickness

kc = filter cake permeability

The permeability of the backfill material can be determined in a laboratory

permeability test (EM 1110-2-1906). The thickness of the backfill is selected

in design (see figure 9-6). The ratio kc/tc is determined from the filter

press test (American Petroleum Institute 1982) using various formation cake

pressures as shown in figure 9-9a. For a range of practical applications, the

ratio kc/tc varies from 5 x 10-9/sec to 25 x 10-9/sec as shown in figure 9-9b. Figure 9-10 shows the permeability of a soil-bentonite slurry trench

cutoff wall 80 cm (about 2-1/2 ft) thick for various values of backfill permeability and ratios of kc/tc . As shown in figure 9-10, the slurry trench

9-25
EM 1110-2-1901

30 Sep 86

a. Schematic of filter press test apparatus

b. Relationship among filter cake permeability, filter cake formation

pressure, and time

Figure 9-9. Determination of filter cake permeability (courtesy of American

Society of Civil Engineers 163 )

9-26
EM 1110-2-1901

30 Sep 86

Figure 9-10. Permeability of a soil-bentonite slurry trench cutoff

wall 80 cm thick for various values of backfill and filter cake

permeability (courtesy of American Society of Civil Engineers 163)

9-27
EM 1110-2-1901

30 Sep 86

permeability is controlled by the backfill when the backfill permeability is

low and by the filter cake when the backfill permeability is high. Also, the

slurry trench permeability has an upper limit of about 10-6 cm/sec even for

very permeable backfill due to the thin low permeability filter cake

(D'Appolonia 1980).

(d) Shear Strength. Soil-bentonite slurry trench cutoffs are difficult

to sample because of their soft nature and very little data are available on

the shear strength of soil-bentonite slurry trench backfill material. For

design purposes, in conducting the stability analysis of the embankment and

foundation, the shear strength of the backfill material is assumed, to be zero.

However, the shear strength of the backfill material does increase with time

due to consolidation and thixotropy. At time of placement, the backfill material will stand on a slope ranging from 1V on 5H to 1V on 10H. This improves

to about 1V on 2H with time (Ryan 1976 and D'Appolonia 1980). The results of

shear strength tests (see table 9-5) on undisturbed samples taken from the

soil-bentonite slurry trench at Saylorville Dam, Iowa, show that the undrained

shear strength of the slurry backfill about a year after placement was 0.10 to

0.12 tons/sq ft (U. S. Army Engineer District, Rock Island 1978b).

(e) Compressibility. The compressibility of the soil-bentonite slurry

trench backfill material depends primarily on the percentage of granular

particles in the gradation as shown in figure 9-11. Low permeability and low

compressibility are contradictory requirements because the plastic fines

required for low permeability result in higher compressibility. Relatively

low compressibility results when there is sufficient granular material in the

backfill to allow grain-to-grain contact between the granular particles

(D'Appolonia 1980).

(f) Mix Design. The gradation of the backfill for the soil-bentonite

slurry trench is selected by conducting permeability, shear strength, and compressibility tests on a range of materials including soil to be excavated from

the trench. Such a procedure was followed in the mix design for the backfill

of the soil-bentonite slurry trench installed for remedial seepage control at

Addicks Dam, Texas (U. S. Army Engineer District, Galveston 1977c). The allowable range set on the gradation of the backfill should produce a material which

contains enough fines to reduce the seepage through the slurry trench cutoff to

an acceptable level and sufficient coarse particles to approximate the strength

and compressibility of the surrounding ground. If sufficient fines are not

present in material excavated from the trench, borrow sources should be identified or alternatively a higher bentonite content specified for the backfill.

If sufficient coarse particles are not present in material excavated from the

trench, approved sources should be identified for obtaining natural sound,

hard, durable sand and gravel. Crushed limestone, dolomite, or other crushed

calcareous materials should not be used. The maximum particle size of the

gravel shall be 3 in. and the material should be well graded.

(5) Cement-Bentonite Slurry Trench Cutoff.

9-28
9-29

Table 9-5. Summary of Shear Strength Data from Post-Construction Testing of Backfill Material from Soil-B

Slurry Trench Cutoff at Saylorville Dam, Towa(a) 

Triaxial 

Atterberg Dry Moisture Time g 

Boring Depth Unified Limits Density Content Construction Sampling 0 c 

No. Station ft Soil Classification LL PL PI lb/cu ft % to to Testing tons/

STU-1 58+90 26.7-28.9 Gravelly clayey 

sand, SC 33 14 19 ll8.2 13.3 8.5 5 4.5 0.0

STU-I 58+90 39.2-41.4 Clayey sand, sc 33 14 19 108.5 17.5 8.5 5 0 0.1

STU-2 64+00 14.5-16.6 Clayey sand, sc 36 15 21 103.5 21.0 8 5 0 0.0

STU-1 58+90 49.2-51.4 Clayey sand, sc 41 17 24 107.9 18.9 8.5 19 STU-2 64+00 32.o-34.3 Clayey sand, sc 33 14 19 114.1 14.9 8 19 STU-6 82+90 16.0-18.1 Gravelly clayey 

sand, SC 34 15 19 120.1 16.9 ll.S 7.5 0 0.1

STU-6 82+90 49.9-51.9 Gravelly clayey 7.5 0 0.1

sand, SC 37 15 22 113.1 17.7 11.5 

STU-7 87+80 17.o-l9.0 Gravelly clayey 6 0 0.1

sand, sc 32 17 15 113.5 17.6 11 

STU-6 82+90 35.4-35.6 Sandy clay, CL 31 18 l3 117 .o 13.1 ll.5 9.5 STU-7 87+80 26.6-28.8 Clayey sand, SC 28 14 14 112.9 19.2 11 11.5 

( ) 106 a From U. s. Army Engineer District, Rock Island (b) Conducted on undisturbed soil specimens 5 in. in diameter by 11 in. high; unconsolidated-undrained (Q) and consolid

·pore pressure measurements (R) shear tests. 
EM 1110-2-1901

30 Sep 86

Figure 9-11. Relationship between fines content and compressibility of a soil-bentonite slurry trench backfill (courtesy

of American Society of Civil Engineers163)

9-30

e PLASTIC FINES 

0 NON-PLASTIC FINES 

~ / 

/ 

• 

e / 1-D COMPRESSION 

0 / 

/e 

STRESS INCREMENT 

0.5 TO 2.0 kg /cm2 

0 ~~--~--~--~--~~~~--~--~--~--~~ 

0 

80 

70 

60 0 

50 

40 

30 

20 

10 

0 0 

0 

.02 .04 .06 .08 .10 

COMPRESSION RATIO, Cc/ I+ e0 

0 

/. .~ 

/ 0./ • ISOTROPIC COMPRESSION 

:;t . 

/ 

.02 .04 .06 

STRESS INCREMENT 

0.5 T02.0 kg/cm2 

.08 .10 

COMPRESSION RATIO, Cc/ I+ e0 

.12 

.12 
EM 1110-2-1901

30 Sep 86

(a) General. If backfill for the slurry trench is not available or is

prohibitive in cost or if the cutoff is deep and the foundation is prone to

failure during excavation, the cement-bentonite slurry trench cutoff may be

more applicable (see table 9-3).

(b) Design Considerations. The primary design parameters are continuity, set time, resistance to hydraulic pressure, permeability, shear strength,

and compressibility.

(c) Continuity. When cement-bentonite slurry trench cutoffs are constructed in panels rather than in a continuous trench, there is a possibility

for unexcavated portions of the trench to remain between the panels. To prevent this the clamshell bucket is moved both vertically and horizontally

throughout each slot at the completion of slot excavation. Also, when the

connecting area between the initial and subsequent panels is excavated, a portion of the adjacent set panels is removed to ensure that all intervening soil

has been excavated (Spooner et al. 1982).

(d) Set Time. The set time is important because of the construction

technique employed. After the cement-bentonite slurry in the first set of

panels has set, the areas between them can be excavated. A normal cementbentonite mixture begins to set after a few hours and has a consistency similar to lard after 12 hours. The second day the cement-bentonite slurry can be

walked on and final set is normally taken at 90 days (Ryan 1977).

(e) Resistance to Hydraulic Pressure. Once the slurry trench has been

completed, the embankment constructed, and the reservoir filled, there is a

substantial differential head acting on the slurry trench (see table 9-2 for

typical values). The time between completion of the slurry trench and reservoir filling is generally sufficiently long (> 90 days) to allow the cementbentonite slurry trench to develop its final set. The resistance of the

cement-bentonite material to withstand gradients comparable to those which

will exist in the field should be tested in the laboratory by subjecting

intact specimens which have developed full set to hydraulic pressure and

measuring the increase (if any) of permeability with time (Spooner et al. 1982

and Jefferis 1981).

(f) Permeability. Although there is some buildup of concentration near

the sides of the cement-bentonite slurry trench, the cement-bentonite does not

form a low permeability cake. The permeability of the slurry trench is a

function of the concentrations of cement, bentonite, sand, and gravel (suspended during the excavation process) in the completed wall (Ryan 1977). The

amount of sand and gravel in the cement-bentonite trench cutoff may range from

10 to 60 percent by dry weight, depending on the foundation material and

method of construction, and generally increases with depth (Dank 1981). If

the trench is excavated under a conventional bentonite slurry which is then

replaced by a cement-bentonite slurry, the sand and gravel content will be low

(10 to 18 percent was measured on undisturbed samples taken from the San

Lorenzo Dam, El Salvador; Dank 1981). Alternatively, if the trench is excavated under a cement-bentonite slurry which is left in the trench to set up and

form the cutoff, the sand and gravel content will be relatively high. Also, if

the trench is excavated under a cement-bentonite slurry, the slurry loss into

9-31
EM 1110-2-1901

30 Sep 86

the surrounding ground will be higher than normal and in some instances as

great as 100 percent of the trench volume (Xanthakos 1979). For design

purposes, specimens should be prepared from the cement-bentonite with varying

percentages of sand and gravel, cured for 28 days under consolidation pressures

existing in the field, and laboratory permeability tests conducted

(EM 1110-2-1906).

(g) Shear Strength. Cement-bentonite slurry trench cutoffs are more

easily sampled and tested than are soil-bentonite slurry walls. Also, specimens of cement-bentonite may be cast in the laboratory and tested. The

results of shear strength tests (see table 9-6) on undisturbed samples taken

from the cement-bentonite slurry trench at Tilden Tailings Project, Michigan,

show the unconfined compressive strength about 6 months after placement

increased with depth ranging from 0.88 to 1.43 tons/sq ft (Dank 1981).

(h) Compressibility. Very little data are available on the compressibility of cement-bentonite slurry trench material (Millet and Perez 1980).

The compressibility should decrease with increase in cement to water ratio

(provided the bentonite is fully hydrated with water prior to adding the

cement) and with increase in sand content (once the concentration of suspended

sand and gravel is sufficient to allow grain-to-grain contact between the

granular materials).

(i) Mix Design. The cement-bentonite slurry trench mixture consists of

water, bentonite, cement, set retarders as necessary, and sand and gravel

entering the trench as a by-product of the excavation. The bentonite should

be fully hydrated with water prior to adding the cement (Millet and Perez

1980). A retarder of the lignosulphite group may be added in small amounts

(0.1 percent) to delay the initial set to avoid hardening of the mix in the

panel before the excavation is completed (Xanthakos 1979). When low permeability is required, the bentonite content of the slurry should be increased

(in the range from 3 to 6 percent by dry weight). Increased sand and gravel

in the slurry will result in an increase in permeability (Dank 1981). The

cement, sand, and gravel content are the chief factors in controlling the

strength and deformability characteristics of the slurry mix (see table 9-6 and

figure 9-12). Generally, the higher the cement to water ratio, the higher the

strength, and more brittle (lower failure strain) the cement-bentonite slurry

mix (Millet and Perez 1980). By varying the bentonite and cement quantities,

flexibility can be designed into the cement-bentonite slurry trench cutoff.

This is especially important if the dam is located at a site where strong

earthquake shocks are likely. The cement-bentonite slurry mix proportions

should be selected by conducting permeability, shear strength, and compressibility tests on a range of materials including soil to be excavated from the

trench. Varying proportions of water, bentonite, cement, sand and gravel

(representing aggregate entering the trench during the excavation process)

should be tested to select a design mix which will reduce the seepage through

the slurry trench cutoff to an acceptable level and approximate the strength

and compressibility of the surrounding ground.

(6) Failure Mechanisms of Cutoffs

9-32
9-33

Table 9-6. Summary of Shear Strength Data from Post-Construction Testing 

of Cement-Bentonite Slurry Trench Cutoff at Tilden Tailings Project, Michigan (a) 

Sand Time Elapsed Unconfined Tr

Content Moisture Construction Compressive 

Boring Depth Dry Density By Volume Content to Sampling Strength 

_g_ lb/cu ft % months 

1 6.0 26.5 2.5 271.6 6 0.92 

1 10.7 29.4 11.6 151.4 6 0.94 

1 15.9 ]2.1 13.2 141.0 6 0.97 

l 21.0 37.0 11.4 138.8 6 1.02 

1 31.0 )7.5 6.2 129.0 6 1.02 

1 4J..O 40.0 115.8 6 

2 6.9 21.4 0.0 236.0 6 0.88 

2 10.8 43.0 6.2 201.0 6 1.00 2 16.0 38.3 11.4 134.5 6 1.14 2 21.0 39.0 13.4 117.1 6 1.30 

(a) From Northwestern University 

(b) Conducted on undisturbed soil specimens; consolidated-drained (S) shear test 
EM 1110-2-1901

30 Sep 86

Figure 9-12. Strength and deformation characteristics of

cement-bentonite slurries (courtesy of American Society

of Engineers223)

9-34

100 

80 

60 

40 

~ 

.... 20 0" 

1: 

41 

l< 

... 

\1'1 

., 0 > 

-

"' "' 41 

... 

0. 

E 

0 140 

u ... ..... c: 

"' ... .... ...... X .0 .., ..... 120 ... 

c: . :::::1 

Cl 

r;,? .... 

.., 

E 100 .... 

.... 

..... 

:::::1 

>. 

., 

Q 80 I 

a! 

.... 

60 

40 

20 

0 

I I 

rl 

f- Bentonite Type I 

r. e SPV 200 I • UG 180 

I - I 

., 

I 

• I 

/ 

-

0 O.l'J o. 20 0. 30 0.40 0.50 0.60 

Cement-Water Ratio C/W 

I I I I 

\ LEGEND 

t\. • Slurry prepared in the laboratory -

~:\ o Slurry sampled during constrUction 

0 

•,\ ' ' ' ~ 

~ ' 

'~ .. ' ........ ', ~ ......... 

• ....... 

i' .• ""' J -0 -.._ ' ~ - ' 00 

' ~ :~ 1 

' t-0 • • '-,., 

~"-, 

............. nf~>.ZS"% • ..... 

5 10 15 20 25 30 

28-oay Triaxial Compressive Strain at Failure 

c:f' 
EM 1110-2-1901

30 Sep 86

(a) Introduction. Several mechanisms can affect the functioning of

slurry walls and cause failure. Failure may occur during excavation of the

trench, upon first filling of the reservoir with the resulting rise in differential head acting across the slurry wall, or at some future time due to

adverse chemical substances in the soil and ground water. Specific failure

mechanisms include trench collapse, gaps (or windows) in the slurry wall,

inadequate aquiclude key-in, blowout or piping of backfill material into the

surrounding pervious foundation, and chemical destruction of the slurry wall

(Spooner et al. 1982).

(b) Trench Collapse. Trench collapse is caused by instability of the

trench walls during excavation and before backfilling (for soil-bentonite

slurry trench) or setup (for cement-bentonite slurry trench). Causes of trench

collapse include failure to maintain the minimum differential head between the

top of the slurry and the top of the ground water and/or too low unit weight of

slurry (see figure 9-7). Drop in the slurry level in the trench may be caused

by contact with gravel, fissures, etc., during excavation, while rise in the

ground-water level may be caused by surface runoff into cracks adjacent to the

trench, particularly following heavy rainfall. Too low unit weight of the

slurry may be caused by the cessation of agitation by excavation equipment over

the week end (Spooner et al. 1982). Such a set of circumstances contributed to

the collapse of a portion of one wall of a soil-cement bentonite slurry trench

at Duncan Dam in Canada (Duguid et al. 1971).

(c) Gaps (or Windows) in the Slurry Wall. Trench collapse or improper

placement of backfill can create gaps (or windows) which result in zones of

higher permeability as well as variations in wall thickness and strength

(Spooner et al. 1982). The continuity of the trench should be tested before

backfilling by passing the bucket or clamshell of the excavating tool vertically and horizontally along each segment of the trench. As mentioned previously, for soil-bentonite slurry trenches irregularities in the backfill

slope are indications that pockets of clean material (slurry not mixed in

properly or was washed out) or slurry were trapped in the backfill or that the

backfill does not contain sufficient sand or coarse material.

(d) Inadequate Aquiclude Key-In. As discussed previously, inadequate

aquiclude key-in will permit seepage under the cutoff. Inadequate key-in can

result from variations in trench depth, insufficient aquiclude penetration,

trench collapse, or the presence of boulders (Spooner et al. 1982).

(e) Blowout or Piping of Backfill Material. As mentioned previously,

blowout or piping of backfill material into the surrounding pervious foundation is especially critical for soil-bentonite slurry trenches when the foundation contains openwork gravel. The required width of the slurry trench to

prevent blowout (factor of safety of 3) in openwork gravel may be estimated

from Equation 9-11.

(f) Chemical Destruction of the Slurry Wall. Chemical substances in

the foundation soil and ground water can affect the durability of the slurry

wall once it is constructed. If salt water is present in the construction

area, appapulgite may be used instead of bentonite. Permeation of a soilbentonite or cement-bentonite slurry wall by polluted ground water generally

9-35
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leads to increased permeability. The bentonite may become entrained in the

solution and the cement may become slurry solubilized as a solution channel is

created through the slurry wall and into the foundation. Chemicals may also

prevent the slurry from forming an adequate filter cake along the sides of the

soil-bentonite slurry trench (Spooner et al. 1982). Where polluted ground

water is present, long-term permeability tests should be conducted using the

specific soil-bentonite backfill materials or cement-bentonite mix from the

site permeated by the actual pollutant in designing the slurry trench cutoff

(Spooner et al. 1982 and D'Appolonia 1980).

(7) Instrumentation and Monitoring.

(a) Introduction. Whenever a slurry trench is used for control of

underseepage, the initial filling of the reservoir must be controlled and

instrumentation monitored to determine if the slurry trench is performing as

planned. If the slurry trench cutoff is ineffective, remedial seepage control

measures must be installed prior to further raising of the reservoir pool

(EM 1110-2-2300).

(b) Parameters of Interest. There are two parameters of interest with

regard to slurry trench cutoffs for control of underseepage. These are the

drop in piezometric head from upstream to downstream across the trench during

reservoir filling and the differential settlement between the top of the

slurry trench and the overlying compacted embankment material.

(c) Efficiency of Slurry Trench Cutoff. To evaluate the head efficiency (see equation 2) of the slurry trench cutoff, the head loss is determined between points immediately upstream and downstream of the slurry trench

cutoff wall at its junction with the base of the dam. The head loss is

established from piezometer readings taken during construction, before and

during initial filling of the reservoir, and subsequently as frequently as

necessary to determine changes that are occurring and to assess their implications with respect to safety of the dam (see Chapter 13). Equal numbers of

piezometers are normally placed on each side of the slurry trench cutoff.

Piezometers should be installed at two or more locations along the length of

the slurry trench depending upon the foundation conditions at the site.

Pneumatic piezometers installed upstream and downstream of the soil-bentonite

slurry trench at West Point Dam, Alabama and Georgia, showed a near-horizontal

piezometric surface existed across the trench prior to filling the reservoir.

Piezometer readings taken after reservoir filling indicated a drop in piezometer head from upstream to downstream across the slurry trench, confirming the

effectiveness of the cutoff (U. S. Army Engineer District, Savannah 1979).

Open-tube piezometers installed upstream and downstream of the soil-bentonite

slurry trench at Addicka Dam, Texas, indicated a drop in piezometric head

across the slurry trench (U. S. Army Engineer District, Galveston 1983).

(d) Differential Settlement. The differential settlement between the

top of the slurry trench and the overlying compacted embankment material is

important because a separation of materials in this region could result in

piping at the interface between the embankment and the foundation. Settlement

plates placed on top of the soil-cement bentonite slurry trench at West Point

Dam, Alabama and Georgia, indicated a uniform total settlement of approximately

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0.5 ft throughout the trench. Excavation of a portion of the trench prior to

filling the reservoir showed no void between the slurry trench backfill and the

overlying compacted fill (U. S. Army Engineer District, Savannah 1968 and

1979).

e. Concrete Wall.

(1) Introduction. When the depth of the pervious foundation is excessive (< 150 ft) and/or the foundation contains cobbles, boulders, or cavernous

limestone, the concrete cutoff wall may be an effective method for control of

underseepage. Using this method, a cast-in-place continuous concrete wall is

constructed by tremie placement of concrete in a bentonite slurry supported

trench. Two general types of concrete cutoff walls, the panel wall and the

element wall have been used, as shown in figures 9-13 and 9-14, respectively.

Since the wall in its simpler structural form is a rigid diaphragm, earthquakes could cause its rupture; therefore, cutoff walls should not be used at

a site where strong earthquake shocks are likely (U. S. Army Engineer

District, Pittsburgh 1965).

(2) History of Use. Conventional (excavated without bentonite slurry)

concrete cutoff walls were widely used prior to 1925. Since they require

about the same excavation and dewatering as compacted backfill trenches and

the wall itself is far more expensive than compacted soil, the popularity of

conventional concrete cutoff walls has declined (Sowers 1962 and Sherard et al.

1963). The method of excavating trenches supported by bentonite for the construction of cast-in-place concrete cutoff walls was used for the first time

in 1951 at the Volturno-Garigliano hydroelectric plant on the Volturno River

at Venafro, near Naples, Italy (Veder 1963, Veder 1975 and Franke 1954). Since

the 1950's, concrete cutoff walls constructed by tremie placement of concrete

in a bentonite slurry supported trench have been used for projects throughout

the world. The deepest concrete cutoff wall to date was constructed at

Manicouagan 3 Dam in Quebec, Canada, in 1972, where two parallel concrete

walls, 2 ft thick and 10 ft apart, extended 430 ft deep (Anonymous 1972). A

comparison of concrete cutoff walls constructed at Corps of Engineers dams is

given in table 9-7.

(3) Sequence of Construction and Location of Wall. Normally the

embankment is constructed first, followed by the concrete cutoff wall located

upstream of the toe of the dam as was done at Kinzua Dam (formerly Allegheny

Dam) and tied into the core of the dam with an impervious blanket (U. S. Army

Engineer District, Pittsburgh 1965). The upstream location minimizes the possibility of compressive failure of the concrete cutoff wall due to negative

skin friction as the foundation settles under the weight of the embankment (as

would occur is the cutoff wall is located under the center of the dam). Constructing the embankment first, followed by the concrete cutoff wall, minimizes

the possibility of rupture of the concrete cutoff wall due to horizontal movement of the foundation as the embankment is constructed. For remedial seepage

control of existing dams (see Chapter 12) where it is not practical to draw

down the reservoir and primary consolidation of the foundation has been

complete, a central location for the concrete cutoff wall may be feasible.

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Figure 9-13. Construction procedure for concrete cutoff wall at

Kinzua Dam (formerly Allegheny Dam), Pennsylvania (after U. S.

Army Engineer District, Pittsburgh 103)

(4) Design Considerations. The primary design parameters are permeability, strength, and compressibility. (1) The permeability is usually

sufficiently low (=10-10 cm/sec for water-cement ratio of 0.6) to reduce the

seepage through the concrete cutoff wall to an acceptable value (Xanthakos

1979). The concrete cutoff wall is generally stronger (>3,000 psi compressive

strength) than the surrounding foundation soil and introduces a heterogeneous

zone (in the form of a rigid diaphragm) in the foundation. The compressibility

of the concrete cutoff wall is sufficiently low that the wall is essentially

rigid with respect to the surrounding foundation soil (Xanthakos 1979).

(a) Permeability. For workable concrete mixes used in concrete cutoff

walls (see table 9-8), the permeability increases rapidly for water-cement

ratios higher than 0.5. For a concrete mix with maximum coarse aggregate size

(1) The workability of the concrete, discussed under Mix Design, is of primary

importance with respect to tremie placement of the concrete.

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a. Excavation procedure for primary and secondary elements

b. Interlocking of primary

and secondary elements

Figure 9-14. Construction procedure for concrete cutoff wall at Wolf

Creek Dam, Kentucky (courtesy of American Society of Civil

160 Engineers )

9-39
9-40

Table 9-7. Comparison of Corps of Engineers Concrete Cutoff Walls 

t.;utorr 

Max. Max. (a) 

Dif- Devifer- at ion Max. 

Date Embankment- ential Max. from Head 

Con- Foundation Head Width Depth Ver- Cutoff 

Project Location structed Material ft. ft ....!!__ Location tical Width 

Kinzua (formerly Allegheny River 1964 Silts, 140 2.5 185 Upstream 1:370 56.0 U

Allegheny) Dam Pennsylvania sands and of toe E

gravels, of dam P

boulders 

Wolf Creek Dam(b) Cumberland River 1978 Embankment 187 2.0 300 Center of 1:600 93.5 U

Kentucky (200ft.); dam E

cavernous N

limestone F

(100 ft.) 

Mill Creek Dam Mill Creek 1981 Silt 51 2.0 170 Upstream 1:100 25.5 U

Washington overlying toe of E

cot)glomerate dam W

Clemson Lowerb Hartwe 11 Lake 1982 Embankment 44 2.0 85 Center of 1:100 22.0 u

Diversion Dam Georgia and (50 ft.); dam E

South Carolina silty sand S

and sand 

(35 ft) 

(a) (b) Deviation from vertical in any direction at any depth. 

Concrete cutoff installed as remedial seepage control for existing dam (see Chapter 12). 
9-41

Table 9-8. Comparison of Concrete Mix Proportions for Corps of Engineers Concrete Cu

28 Day Compre

Cement(a) Aggregate lb/s

Fly Ash Water Water/Cement lb/cu ;ld Slump 

Project lb/cu lb/cu lb/cu xd + Ash Coarse Fine in. SEec

Kinzua (formerly 564 0 292 0.52 1,652 1,345 7 3,0

Allegheny Dam) 

Wolf Creek Dam 564 123 275 0.40 1,619 1,369 6.5-7.5 3,0

Mill Creek Dam 299 l34(b) 260 0.60 1,628 1,587 8 1,5

Clemson Lower 507 110 334 0.54 1,540 1,310 60.9.0 1,3

Diversion Dam 

(a) (b) Weights are saturated surface dry. 

Fly ash percentage replaced by solid volume was raised from 35 to 45 before wall was comp
EM 1110-2-1901

30 Sep 86

of 3/4 in. and a water cement ratio of 0.6, the permeability is usually lower

than 10-10 cm/sec (Xanthakos 1979). The permeability of a concrete cutoff

wall is influenced by cracks in the finished structure and/or by void spaces

left in the concrete as a result of honeycombing or segregation (see Equation 9-4 and figure 9-5). The joints between panels are not completely

impermeable but the penetration of bentonite slurry into the soil in the

immediate vicinity of the joint usually keeps the flow of water very small

(Hanna 1978). Measured head efficiency for concrete cutoff walls from

piezometric data generally exceeds 90 percent (Telling, Menzies, and Simons

1978b). At Kinzua Dam (formerly Allegheny Dam), the measured head efficiency

was 100 percent, i.e., the head just downstream of the concrete cutoff wall was

of the magnitude established by vertical seepage through the upstream

connecting blanket (Fuquay 1968).

(b) Strength. The compressive strength for concrete cutoff walls is

generally specified to exceed 3,000 lb/sq in. (see table 9-8). Therefore, the

concrete cutoff wall is generally stronger than the surrounding foundation

soil. The most important factor influencing the strength of the concrete is

the water-cement ratio. The concrete's fluidity, i.e., ability to travel

through the tremie and fill the excavation, also depends upon the water-cement

ratio. Too low a water-cement ratio would decrease flowability and increase

compressive strength. Too high a water-cement ratio would promote segregation. A good balance is achieved with a water-cement ratio near 0.5 which

results in a 28-day compressive strength exceeding 3,000 lb/sq in. (see

table 9-8). Cement continues to hydrate and concrete continues to increase in

compressive strength, at a decreasing rate, long after 28 days (Winter and

Nilson 1979).

(c) Compressibility. The concrete cutoff wall is essentially rigid and

has low compressibility compared to the surrounding foundation soil. The

modulus of elasticity for concrete cutoff walls may be approximated from

(Winter and Nilson 1979)

(9-13)

where

= modulus of elasticity in lb/sq in.

W = unit weight of concrete in lb/cu ft

= compressive strength of concrete in lb/sq in.

(5) Mix Design. In addition to strength, workability is an important

requirement for the concrete mix. The mix must not segregate during placement. Too high a water-cement ratio or too low a cement content (with a good

water-cement ratio) will tend to segregate. Natural well rounded aggregate

increases flowability and allows the use of less cement than an angular

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manufactured aggregate. Since the concrete is poured into the trench through

tremie pipes and displaces the bentonite slurry from the bottom of the excavation upward, the concrete must have a consistency such that it will flow

under gravity and resist mixing with the bentonite slurry. Admixtures may be

used as required to develop the desired concrete mix characteristics. Fly ash

is often used to improve workability and to reduce heat generation. The unique

problems inherent at each project require studies to develop an adequate concrete mix (Holland and Turner 1980). Some typical concrete mixes used in Corps

of Engineers concrete cutoff walls are given in table 9-8. The placement

techniques used for the concrete are of equal importance in assuring a satisfactory concrete cutoff wall.

(6) Excavation and Placement of Concrete. Temporary guide walls are

constructed at the ground surface to guide the alignment of the trench and

support the top of the excavation. Typically, a cross section, 1 ft wide and

3 ft deep, is sufficient for most concrete cutoff walls. In order to ensure

continuity between panels and provide a watertight joint to prevent leakage,

an appropriate tolerance is placed on the maximum deviation from the vertical

(see table 9-7). The same general requirements apply to the slurry used to

keep the trench open for concrete cutoffs. As stated previously, two general

types of concrete cutoff walls, the panel wall, and the element wall have been

used. The panel wall is best suited for poorly consolidated materials and soft

rock can be installed to about a 200-ft depth. The element wall has the

advantage of greater depth (430 ft deep at Manicouagan 3 Dam in Quebec,

Canada), better control of verticality, the ability to penetrate hard rock

using chisels and/or nested percussion drills, and the protection of the

embankment with casing when used for remedial seepage control. However, the

element wall is more costly and has a slower placement rate than the panel

wall. Both types of concrete cutoff walls open short horizontal sections of

the embankment and/or foundation at a time, which limits the area for potential

failure to a segment that can be controlled or repaired without risking

catastrophic failure of the project. The concrete cutoff wall penetrates the

zone(s) of seepage with a rigid, impermeability barrier capable of withstanding

high head differentials across cavities with no lateral support. The concrete

must be placed at considerable depth through bentonite slurry in a continuous

operation with as little contamination, honeycomb, or segregation as possible.

The bottom of the excavation must be cleaned so that a good seal can be

obtained at grade. Fresh bentonite slurry is circulated through the excavation

to assist in the cleaning and lower the density of the slurry to allow the

concrete to displace the slurry easier once placement begins. The tremie

procedure used to place the concrete is straightforward in theory and yet often

in practice causes more problems with the final quality of the concrete cutoff

wall than any other factor. The tremie system consists of a hopper, tremie

pipe, and a crane or other lifting equipment to support the apparatus. The

hopper should be funnel shaped and have a minimum capacity of 0.5 cu yd. The

size of the tremie pipe depends upon the size of aggregate used in the concrete

mix. For 3/4-in. maximum diameter coarse aggregate, a 10-in.-diam tremie pipe

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should be used. (1) The dry tremie is placed in the hole with a metal plate and

rubber gasket wired to the end of the tremie. The tremie pipe is lifted,

breaking the wires and allowing the concrete flow to begin. Concrete is added

to the hopper at a uniform rate to minimize free fall to the surface in the

pipe and obtain a continuous flow. The tremie apparatus is lifted during

placement at a rate that will maintain the bottom of the pipe submerged in

fresh concrete at all times and produce the flattest surface slope of concrete

that can practically be achieved. The flow rate (foot of height per hour) and

surface slope of the concrete shall be continuously measured during placement

with the use of a sounding line. A sufficient number of tremies should be

provided so that the concrete does not have to flow horizontally from a tremie

more than 10 ft. As soon as practical, core borings should be taken in

selected panels through the center of the cutoff wall to observe the quality of

the final project. Unacceptable zones of concrete such as honeycombed zones,

segregated zones, or uncemented zones found within the cored panels or elements

should be repaired or removed and replaced. One means of minimizing such

problems at the start of a job is to require a test section in a noncritical

area to allow changes in the construction procedure to be made early in the

project (Hallford 1983; Holland and Turner 1980; and Gerwick, Holland, and

Komendant 1981).

(7) Treatment at Top of Concrete Cutoff Wall. As mentioned previously,

normally the concrete cutoff wall is located under or near the upstream toe of

the dam and tied into the core of the dam with an impervious blanket. If a

central location for the concrete cutoff wall is dictated by other factors,

the connection detail between the top of the concrete cutoff wall and the core

of the dam is very important. Generally, the concrete cutoff wall extends

upward into the core such that, the hydraulic gradient at the surface of the

contact does not exceed 4 (Wilson and Marsal 1979). Various precautions (see

figure 9-15) have been taken to prevent the top of the concrete cutoff wall

from punching into the core of the dam and causing the core to crack as the

foundation settles on either side of the rigid cutoff wall under the weight of

the embankment. The bentonite used at the connection between the concrete

cutoff wall and the core of the dam (see figure 9-15) is intended to create a

soft zone to accommodate differential vertical settlements of the core around

the concrete cutoff wall. Also, saturation of the bentonite is intended to

produce swelling which will provide for a bond between the core and the concrete cutoff wall to prevent seepage (Radukic 1979).

(8) Failure Mechanisms of Concrete Cutoff Walls. Several mechanisms

can affect the functioning of concrete cutoff walls and cause failure. As

mentioned previously, the wall in its simpler structural form is a rigid

diaphragm and earthquakes could cause its rupture. For this reason concrete

cutoff walls should not be used at a site where strong earthquake shocks are

(1) At Wolf Creek Dam concrete problems (areas of segregated sand or coarse

aggregate, voids, zones of trapped laitance, and honeycombed concrete)

occurred for tremie-placed 26-in. -diam cased primary elements. This must

be considered in future projects which involve tremie-placed elements of

small cross-sectional areas (Holland and Turner 1980).

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a. Forked connection

c. Piston connection

b. Plastic impervious cap

d. Double wall connection

Figure 9-15. Connections between concrete cutoff wall

and core of dam (courtesy of ICOS

182 )

9-45
EM 1110-2-1901

30 Sep 86

likely. Concrete cutoff walls located under or near the toe of the dam are

subject to possible rupture from horizontal movements of the foundation soil

during embankment construction. This effect can be minimized by constructing

the dam embankment prior to the concrete cutoff wall. As mentioned previously,

concrete cutoff walls located under the center of the dam are subject to possible compressive failure due to negative skin friction as the foundation

settles under the weight of the embankment. The probability of this occurring

would depend upon the magnitude of the negative skin friction developed at the

interface between the concrete cutoff wall and the foundation soil and the

stress-strain characteristics of the concrete cutoff wall. Also, as previously

mentioned, a centrally located concrete cutoff wall may punch into and crack

the overlying core material unless an adequate connection is provided between

the concrete cutoff wall and the core of the dam.

(9) Instrumentation and Monitoring. Whenever a concrete cutoff wall is

used for control of underseepage, the initial filling of the reservoir must be

controlled and instrumentation monitored to determine if the concrete cutoff

wall is performing as planned. If the concrete cutoff wall is ineffective,

remedial seepage control measures must be installed prior to further raising

the reservoir pool. When the embankment is constructed first, followed by the

concrete cutoff wall located upstream of the toe of the dam, as was done at

Kinzua (formerly Allegheny Dam), the parameters of interest are the drop in

piezometric head from upstream to downstream across the concrete cutoff wall,

differential vertical settlement between the upstream impervious blanket and

the top of the concrete cutoff wall, and vertical and horizontal movement of

the concrete cutoff wall due to reservoir filling. If a central location for

the concrete cutoff wall is dictated by others factors, the parameters of

interest are the drop in piezometric head from upstream to downstream across

the cutoff wall, differential vertical settlement between the core of the dam

and the top of the concrete cutoff wall, and vertical and horizontal movement

of the concrete cutoff wall due to construction of the embankment and reservoir filling. Instrumentation data should be obtained during construction,

before and during initial filling of the reservoir, and subsequently as frequently as necessary to determine changes that are occurring and to assess

their implications with respect to the safety of the dam (see Chapter 13).

The head efficiency for concrete cutoff walls is evaluated in the same manner

as described previously for slurry trench cutoffs. As previously mentioned,

measured head efficiency for concrete cutoff walls generally exceeds

90 percent.

f. Steel Sheetpiling.

(1) Introduction. Steel sheetpiling is rolled steel members with

interlocking joints along their edges. Sheetpiling is produced in straight

web, arch web, and Z sections in a graduated series of weights joined by

interlocks to form a continuous cutoff wall as shown in figure 9-16. Steel

sheetpiling is not recommended for use as a cutoff to prevent underseepage

beneath dams due to the low head efficiency. Steel sheetpiling is frequently

used in conjunction with concrete flood control and navigation structures to

confine the foundation soil to prevent it from piping out from under the

structure (EM 1110-2-2300 and Greer, Moorhouse, and Millet 1969).

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30 Sep 86

STRAIGHT ARCH Z

a. Sections

b. Interlocking of sections

Figure 9-16. Steel sheetpiling installation (from U. S. Army Engineer

Waterways Experiment Station57)

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(2) History of use. Steel sheetpiling was first used by the Corps of

Engineers to prevent underseepage at Fort Peck Dam, Montana (U. S. Army Engineer District, Omaha 1982). The steel sheetpiling, driven to Bearpaw shale

bedrock with the aid of hydraulic spade jetting, reached a maximum depth of

163 ft in the valley section (see table 9-9). An original plan to force grout

into the interlocks of the steel sheetpiling was abandoned during construction

as impractical. Steel sheetpiling was used as an extra factor to prevent piping of foundation soils at Garrison Dam, North Dakota (U. S. Army Engineer

District, Omaha 1964). At Garrison Dam, underseepage control was provided for

by an upstream blanket and relief wells and the contribution of the steel

sheetpiling to reduction of underseepage was neglected in the design of the

relief wells. Steel sheetpiling and an upstream blanket were installed for

control underseepage at Oahe Dam, South Dakota. Relief wells were installed

for remedial seepage control to provide relief of excess hydrostatic pressures

developed by underseepage (U. S. Army Engineer District, Omaha 1961).

(3) Efficiency of Steel Sheetpiling Cutoffs. The efficiency of steel

sheetpiling cutoffs is dependent upon proper penetration into an impervious

stratum and the condition of the sheeting elements after driving. When the

foundation material is dense or contains boulders which may result in ripping

of the sheeting or damage to the interlocks (see figure 9-17), the efficiency

will be reduced (Guertin and McTigue 1982). Theoretical studies indicate that

very small openings in the sheeting (< 1 percent of the total area) will cause a

substantial reduction in the cutoff efficiency (from 100 to 10 percent efficiency) as shown in figure 9-18 (Ambraseys 1963). The measured head efficiency

for steel sheetpiling cutoffs installed at Corps of Engineers dams is given in

table 9-9. The effectiveness of the steel sheetpiling is initially low, only

12 to 18 percent of the total head was lost across the cutoff as shown in

table 9-9. With time, the head loss across the steel sheetpiling increased to

as much as 50 percent of the total head. This increase in effectiveness is

attributed to migration of fines and corrosion in the interlocks and reservoir

siltation near the dam.

9-5. Upstream Impervious Blanket. (1)

a. Introduction. When a complete cutoff is not required or is too

costly, an upstream impervious blanket tied into the impervious core of the

dam may be used to minimize underseepage. Upstream impervious blankets should

not be used when the reservoir head exceeds 200 ft because the hydraulic

gradient acting across the blanket may result in piping and serious leakage.

Downstream underseepage control measures (relief wells or toe trench drains)

are generally required for use with upstream blankets to control underseepage

and/or prevent excessive uplift pressures and piping through the foundation.

Upstream impervious blankets are used in some cases to reinforce thin spots in

natural blankets. Effectiveness of upstream impervious blankets depends upon

their length, thickness, and vertical permeability, and on the stratification

and permeability of soils on which they are placed (EM 1110-2-2300, Barron

1977 and Thomas 1976).

(1) The blanket may be impervious or semipervious (leaks in the vertical

direction).

9-48
9-49

Table 9-9. Comparison of Corps of Engineers Steel Sheetpiling Cutoff Walla 

Max 

Date Foundation Depth 

Project Location Constructed Materials ...!!..__ Location 

Ft. Peck Dam Missouri River, 1940 Gravels, 163 Center of daa Prevent 

Montana and·silts under seepage 

Garrison Dam I.Ussouri River, 1954 Sand with 110 Upstream Prevent piping 

North Dakota gravel lenses portion of 

dam 

Oahe Dam Missouri River, 1958 Sands, gravels, 75 Upstream Prevent piping 

South Dakota and silts portion of 

dam 

(a) After 17 years (relief wells were installed in 1942 aa remedial underseepage control) 

(b) After 10 years (upstream blanket and relief wells were constructed prior to impoundment) 

Head Efficiency of 

Cutoff, % 

Initial With TiM 

12 lo(a) 

18 50(b) 16 22(c) 

(c) After 4 years (upstream blanket constructed prior to impoundment and relief wells installed in 1962 as remedial underseepag
EM 1110-2-1901

30 Sep 86

Figure 9-17. Sources of leakage associated with steel sheetpile

cutoffs (from U. S. Department of Transportation41)

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30 Sep 86

Figure 9-18. Cutoff efficiency versus open space ratio for

imperfect cutoffs (courtesy of Butterworths, Inc. 129

)

b. Design Considerations. In alluvial valleys, frequently soils consist

of fine-grained top stratum of clay, silt, and silty or clayey sand underlain

by a pervious substratum of sand and gravel. As stated previously, the top

stratum or blanket may be impervious or semipervious (leaks in the vertical

direction). The substratum aquifer or pervious foundation is generally

anisotropic with respect to permeability so the flow is horizontal. For this

condition, shown in figure 9-19, the basic assumptions for the design of upstream impervious blankets are:

(1) Flow through the blanket is vertical.

(2) Flow through the pervious foundation is horizontal.

(3) All flows are laminar and steady state.

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a. Continuous blanket and aquifer

b. Discontinuous upstream blanket, continuous aquifer

L1 = Effective length of upstream natural blanket

L2 = Length of embankment base

L3 = Effective length of downstream natural blanket

Lo = Length of discontinuous upstream blanket

h = Net head to dissipate

Z = Thickness of natural blanket

kb

= Thickness of aquifer

= Permeability coefficient of blanket

kf

= Permeability coefficient of aquifer

d

= Submerged unit weight of blanket

ho

= Pressure head under blanket at downstream toe of dam

hC = Critical head under blanket at downstream toe of dam

Fh = Factor of safety relative to heaving at downstream toe

= Unit weight of water (63.4 pcf)

qf = Rate of discharge through aquifer with unit length normal to the

section

Figure 9-19. Upstream impervious blanket (from U. S. Department of

72 Agriculture )

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(4) The dam (or core of a zoned embankment) is impervious.

(5) Both the blanket and substratum have a constant thickness and are

horizontal.

When the top stratum or pervious foundation consists of several layers of

different soils, they must be transformed into a single stratum with an

effective thickness and permeability (see procedure given in U. S. Army

Engineer Waterways Experiment Station 1956a). For the upstream impervious

blanket shown in figure 9-19, the effective length of the upstream blanket is

where

L1 = effective length of upstream blanket

kf = horizontal permeability of pervious foundation

kb R = vertical permeability of upstream blanket

Zb R = thickness of upstream blanket

d = thickness of pervious foundation

The effective length of the downstream blanket is

where

(9-14)

(9-15)

L3 = effective length of downstream blanket

kbL = vertical permeability of downstream blanket

Zb L = thickness of downstream blanket

Upstream blankets should be designed so that under maximum reservoir

conditions the pressure head under the blanket at the downstream toe of the

dam and the rate of discharge through the pervious foundation are acceptable.

The pressure head under the blanket at the downstream toe of the dam (see

figure 9-19) is

9-53
EM 1110-2-1901

30 Sep 86

(9-16)

where

ho = pressure head under the blanket at the downstream toe of the dam

h = net head to dissipate

L2 = length of impervious core or dam base

The critical pressure head under the blanket at the downstream toe of the dam

is

(9-17)

where

hc = critical pressure head under the blanket at the downstream toe of

the dam

= submerged unit weight of downstream blanket soil

= unit weight of water

The factor of safety against uplift or heaving at the downstream toe of the dam

is

(9-18)

where Fh is the factor of safety against uplift or heaving at the downstream

toe of the dam. Generally dams are designed without relying upon natural

downstream blankets because it is difficult to assure the continuity and the

existence of the blanket throughout the life of the structure. Also, downstream seepage control measures (relief wells or trench drains) are generally

used with upstream blankets to reduce uplift or heaving at the downstream toe

of the dam. However, for the exceptional case where the dam is designed with a

natural downstream blanket and with no downstream seepage control measures

(relief wells or trench drains), upstream blankets should be designed so that

the factor of safety against uplift or heaving at the downstream toe of the dam

is at least 3. The rate of discharge through the pervious foundation per unit

length of dam (see figure 9-19) is

9-54
EM 1110-2-1901

30 Sep 86

(9-19)

where qf is the rate of discharge through the pervious foundation per unit

length of dam. The acceptable rate of discharge or underseepage depends upon

the value of the water or hydropower lost, availability of downstream rightof-way, and facility for disposal of underseepage. The following procedure is

used to determine the length of an upstream blanket when there is a downstream

blanket present (see figure 9-19b):

(a) Determine L1 from equation 9-14 using a conservative value of

kf/kbR , i.e., the highest probable ratio.

(b) Determine

kf/kbL , i.e.,

L3 from equation 9-15 using a conservative value of

the highest probable ratio.

(c) Determine ho , hc , and Fh from equations 9-16, 9-17, and 9-18,

respectively. If Fh < 3.0 , the blanket thickness of

be increased, the permeability of the upstream blanket

decreased by compaction, or downstream seepage control

(d) Determine the rate of discharge through the

unit length of dam from equation 9-19. If the rate of

the upstream blanket may

material may be

measures may be used.

pervious foundation per

discharge is excessive,

a reduction can be obtained by increasing the thickness of the upstream blanket

or reducing the permeability of the upstream blanket material by compaction.

When these methods are used, steps 1 to 4 are repeated before going to step 5.

(e) If the rate of discharge is acceptable, calculate the factor

(9-20)

where c has the units of 1/ft .

(f) Enter figure 9-20 with c and L1 and obtain Lo , which is the

distance from the upstream toe of a homogeneous impervious dam or the impervious core section of a zoned embankment to where a discontinuity in the upstream blanket will have no effect on the uplift at the downstream toe of the

dam or rate of discharge through the pervious foundation. This is the point

beyond which a natural blanket may be removed in a borrowing operation.

Also, Lo would represent the distance upstream from the toe of the dam to

which a streambed should be blanketed to ensure the continuity of a natural

upstream blanket. If there is no downstream blanket the pressure head under

the blanket at the downstream toe of the dam will be zero (see equation 9-16)

9-55
EM 1110-2-1901

30 Sep 86

Figure 9-20. Effective lengths of upstream and downstream impervious blankets (from U. S. Department of Agriculture

72

)

and the following procedure is used to determine the length of the upstream

blanket:

• Assume several values of Lo (length of the upstream blanket from

the upstream toe of a homogeneous impervious dam or the impervious core

section of a zoned embankment).

9-56
EM 1110-2-1901

30 Sep 86

• Calculate c from equation 9-20 using the design thickness and

permeability rates for the constructed blanket and pervious foundation. Note

that c has units of 1/ft.

• Enter figure 9-20 with the assumed values of Lo and the

calculated values of c to obtain the corresponding value of Ll for each

assumed value of Lo .

• Calculate qf from equation 9-19 (L3 = 0 for no downstream

blanket) using the values of L1 obtained from figure 9-20.

• Plot qf versus Lo . The curve will indicate a rapid decrease in

qf with increasing values up to a point where the curve flattens out indicating an optimum length. The upstream blanket can be terminated at any point

where the desired reduction in rate of discharge through the pervious foundation per unit length of dam is achieved (Talbot and Nelson 1979).

c. Materials and Construction. At sites where a natural blanket of

impervious soil already exists, the blanket should be closely examined for

gaps such as outcrops of pervious strata, streambeds, root holes, boreholes,

and similar seepage paths into the pervious foundation which, if present,

should be filled or covered with impervious material to provide a continuous

blanket to a distance Lo from the upstream toe of the dam. Also, as

previously stated, upstream borrow areas should be located greater than the

distance Lo from the upstream toe of the dam so as not to reduce the effectiveness of the natural blanket. Figure 9-21 shows the influence of gaps in

the upstream blanket on relative seepage and uplift at the toe of the dam.

That portion of the upstream blanket placed beneath the embankment to tie into

the impervious core should be composed of the same material and compacted in

the same manner as the core. Upstream of the embankment, the blanket is constructed by placing impervious soil in lifts and compacted only by movement of

hauling and spreading equipment, or to whatever additional extent is necessary

for equipment operation. Exposed clay blankets can shrink and crack after

placement. If such cracks penetrate the blanket, they will reduce the effectiveness of the blanket. Thus it may become necessary to sprinkle the surface

of the blanket to help retain moisture until a permanent pool is impounded. In

higher reaches of abutments which are infrequently flooded by the reservoir, a

thicker blanket may be required so that cracks will not fully penetrate the

blanket. In colder climates, the blanket thickness should be increased to

account for the loosening of the upper part of the blanket by frost action

which substantially increases the permeability.

d. Reservoir Siltation. For some reservoirs, appreciable siltation

occurs which may both increase the thickness of and lengthen the upstream

blanket. Although the siltation may reduce the rate of discharge through the

pervious foundation with time, it is not a factor to be counted upon in design

because the upstream blanket must function adequately following initial filling of the reservoir prior to the occurrence of siltation.

9-57
EM 1110-2-1901

30 Sep 86

c. Relative seepage

a. Cross section of dam

b. Flow net with incomplete blanket (X/L = 0.1)

d. Uplift at toe

Figure 9-21. Effect of gap in upstream blanket on relative seepage

and uplift at toe (courtesy of John Wiley and Sons 155 )

9-6. Downstream Seepage Berms.

a. Introduction. When a complete cutoff is not required or is too

costly, and it is not feasible to construct an upstream impervious blanket, a

downstream seepage berm may be used to reduce uplift pressures in the pervious

foundation underlying an impervious top stratum at the downstream toe of the

dam. Other downstream underseepage control measures (relief wells or toe

trench drains) are generally required for use with downstream seepage berms.

Downstream seepage berms can be used to control underseepage efficiently where

the downstream top stratum is relatively thin and uniform or where no top

stratum is present, but they are not efficient where the top stratum is

relative thick and high uplift pressures develop. Downstream seepage berms

may vary in type from impervious to completely free draining. The selection

of the type of downstream seepage berm to use is based upon the availability

of borrow materials and relative cost of each type.

b. Design Considerations. When the top stratum or pervious foundation

consists of several layers of different soils, they must be transformed into a

single stratum with an effective thickness and permeability (see procedure

given in U. S. Army Engineer Waterways Experiment Station 1956a). Where a

9-58
EM 1110-2-1901

30 Sep 86

downstream natural blanket is present, the downstream seepage berm should have

a thickness so that the factor of safety against uplift or heaving at the downstream toe of the dam is at least 3 and width so that the factor of safety

against uplift at the downstream toe of the seepage berm is at least 1.5.

Formulas for the design of downstream seepage berms where a downstream natural

blanket is present are given in figure 9-22. If there is no downstream natural

blanket present, the need for a downstream seepage berm will be based upon

Bligh's creep ratio.

(9-21)

where

cB = Bligh's creep ratio

Xl = effective length of upstream blanket

L2 = length of dam base

X = width of downstream seepage berm

h = net head on dam

Minimum acceptable values of Bligh's creep ratio are given in table 9-10. If

the creep ratio is greater than the minimum value, a downstream seepage berm is

not required. (1) If the creep ratio is less than the minimum value, the width

of the downstream seepage berm should be made such that the creep ratio is

above the minimum value shown in table 9-10. The thickness of the downstream

seepage berm at the toe of the dam will be determined so that the factor of

safety against uplift or heaving at the downstream toe of the dam is at

least 3. The pressure head beneath the downstream seepage berm at the landside

toe of the levee is

(9-22)

where

ho = pressure head under the seepage berm at the downstream toe of the

dam

(1) A downstream seepage berm may be required to correct other problems such

as excessive seepage gradients under the dam (could be detected by checking the rate of underseepage).

9-59
EM 1110-2-1901

30 Sep 86

d = thickness of pervious foundation

X1 = effective length of upstream natural blanket (taken equal to 0.43d

where no upstream natural blanket exists)

The rate of discharge through the pervious foundation per unit length of dam

is

(9-23)

where

qf = rate of discharge through the pervious foundation per unit length

of dam

kf = horizontal permeability of pervious foundation

As stated previously, the acceptable rate of discharge or underseepage depends

upon the value of the water or hydropower lost, availability of downstream

right-of-way, and facility for disposal of underseepage. Downstream seepage

berms should have a minimum thickness of 10 ft at the dam toe and a minimum

thickness of 5 ft at the berm toe. The computed thickness of the berm should

be increased 25 percent to allow for shrinkage, foundation settlements, and

variations in the design factors. Downstream seepage berms should have a

slope of 1V on 50H or steeper to ensure drainage (U. S. Army Engineer Waterways

Experiment Station 1956a).

c. Materials and Construction. As previously stated, the selection of

the type of material used to construct the downstream seepage berm is based

upon the availability of borrow materials and relative cost of each type. A

berm constructed of impervious soil should be composed of the same material as

the impervious core. That portion of the downstream impervious seepage berm

placed beneath the embankment to tie into the impervious core should be compacted in the same manner as the core. Downstream of the embankment, the

impervious seepage berm is constructed by placing impervious soil in lifts and

compacting only by movement of hauling and spreading equipment, or to whatever

additional extent is necessary for equipment operation. Semipervious material

used to construct downstream seepage berms should have an in-place vertical

permeability equal to or greater than that of the upstream natural blanket and

are compacted in the same manner as described previously for impervious material. Material used in a sand berm should be as pervious as possible, with

a minimum in-place vertical permeability of 100 x 10-4

cm per sec. Downstream

seepage berms constructed of sand should be compacted to an average in-place

relative density of at least 85 percent with no portion of the berm having a

relative density less than 80 percent. As proper functioning of a downstream

seepage berm constructed of sand depends upon its continued perviousness, it

should not be constructed until after the downstream slope of the earth dam has

9-60
9-61

c = 

PeRVIOUS SUBSTRATUM 

NOTATIONS 

h0 = HEAD AT LANDS IDE TOE OF DAM WITHO\.)T s + )(3 

= HEAD AT LANDSIDE TOE OF DAM WITH BERM 

SUBMERGED UNIT WEIGHT OF TOP STRATUM 

SUBMERGED UNIT WEIGHT OF BERM 

i0 = ALLOWABLE UPWARD GRADIENT AT LANDSIDE TOE OF DAM 

i 1 = ALLOWABLE UPWARD GRADIENT AT TOE OF BERM 

UNIT WEIGHT OF WATER 

IMPERVIOUS BERM (k, = 01 

X1 = 

h , =H (: --- x3 +X ) 

o S + x3 +X 

USE F;;. 1.5 

ha "' ALLOWABLE HEAD AT TOE OF BERM = 11 zt 

SEMIPERVIOUS BERM lk1 - k0 ci 

-A + V A 2 - 24(2 + t) (1 + SC- ':!_) Xsp - ha_ 

2C 12 + t) 

WHERE IN· 

A= 6 + 3 SC (r + 1) 

h;,- 10 Z1 t=---

1 + i0 

FORMULAS 

SAND BERM 

X 

X = REQUIRED BERM WIDTH 

t = REQUIRED THICKNESS OF BERM AT 

k1 = VERTICAL PERMEABILITY OF BERM 

F = FACTOR OF SAFETY AGAINST UPLIF

OF DAM 

0 8 = FLOW INTO BERM PER FT OF DAM 

PERVIOUS BERM WITH COLL

, Hx h=h=--3 

0 0 s + )(3 

1i 

1+--

F 1w 

0 (1 

B S + x3 

Figure 9-22. Design of downstream seepage berms where a downstream natural blan

present (from U.S. Army Engineer Waterways Experiment Station120) 
EM 1110-2-1901

30 Sep 86

Table 9-10. Minimum Bligh's Creep Ratios for Dams

Founded on Pervious Foundations (a)

Material

Very fine sand or silt

Fine to medium sand

Coarse sand

Fine gravel or sand and gravel

Coarse gravel including cobbles

Minimum Bligh's

Creep Ratio

18

15

12

9

(a) From U. S. Army Engineer Waterways Experiment

Station120

become covered with sod and stabilized so that soil particles carried by surface runoff and erosion will not clog the seepage berm. If it is necessary to

construct the downstream seepage berm at the time the earth dam is built or

before it has become covered with sod, an interceptor dike should be built at

the intersection of the downstream toe of the dam and the seepage berm to prevent surface wash from clogging the seepage berm. A free-draining downstream

seepage berm is one composed or random fill overlying horizontal sand and

gravel drainage layers with a terminal perforated collector pipe system (U. S.

Army Engineer Waterways Experiment Station 1956a).

9-7. Relief Wells.

a. Introduction. When a complete cutoff is not required or is too

costly, relief wells installed along the downstream toe of the dam may be used

to prevent excessive uplift pressures and piping through the foundation.

Relief wells increase the quantity of underseepage from 20 to 40 percent

depending upon the foundation conditions. Relief wells may be used in combination with other underseepage control measures (upstream impervious blanket

or downstream seepage berm) to prevent excessive uplift pressures and piping

through the foundation. Relief wells are applicable where the pervious foundation has a natural impervious cover. The well screen section (see figure 9-23), surrounded by a filter if necessary, should penetrate into the

principal pervious stratum to obtain pressure relief, especially where the

foundation is stratified. The wells, including screen and riser pipe, should

have a diameter which will permit the maximum design flow without excessive

head losses but in no instance should the inside diameter be less than

6 in. Filter fabrics should not be used in conjunction with relief wells (see

Appendix D). Even in nearly homogeneous stratum, a penetration of less than

50 percent results in significant rise in pressure midway between adjacent

wells, or requires close spacing. Relief wells should be located so that

9-62
EM 1110-2-1901

30 Sep 86

Figure 9-23. Typical relief well (after EM 1110-2-1913)

9-63

METAL WELL GUARD -

VARIABLE- TO TOP OF 

MINIMUM WATER TABLE 

RISER PIPE 

. . . 0 •• 

0 

••• 

V-lWTCH WEIR 

SAND BACKFILL 

TOF' OF 

GRAVEL FILTER 

0 0" 

• 0 

0 °• o TOP OF •:o~ WELL SCREEN •• 0 

o•. 

0 .. 

-~+---- 0 0 • 

e• 0 o • 0 .o • 0 

•• 0 

... 

BLANK PIPE 

THROUGH VERY 

FINE SAND STRATA 

GRAVEL FILTER 

~ l L.:.'-'·'-. ::::::__;;._.o 

PERFORATED OR 

SLOTTED SCREEN 

BOTTOM PLUG 

MIN 
EM 1110-2-1901

30 Sep 86

their tops are accessible for cleaning, sounding for sand, and pumping to

determine discharge capacity. Relief wells should discharge into open ditches

or into collector systems outside of the dam base which are independent of toe

drains or surface drainage systems. Experience with relief wells indicates

that with the passage of time the discharge of the wells will gradually

decrease due to clogging of the well screen and/or reservoir siltation. A

comprehensive study of the efficiency of relief wells along the Mississippi

River levee showed that the specific yield of 24 test wells decreased 33 percent over a 15-year period. Incrustation on well screens and in gravel filters

was believed to be the major cause (Montgomery 1972). Therefore, the amount of

well screen area should be designed oversized and a piezometer system installed

between the wells to measure the seepage pressure, and if necessary additional

relief wells should be installed (EM 1110-2-2300, U. S. Army Engineer Waterways

Experiment Station 1956a, Singh and Sharma 1976).

b. History of Use. The first use of relief wells to prevent excessive

uplift pressures at a dam was by the U. S. Army Engineer District, Omaha, when

21 wells were installed from July 1942 to September 1943 as remedial seepage

control at Fort Peck Dam, Montana. The foundation consisted of an impervious

stratum of clay overlying pervious sand and gravel. Although a steel sheetpile

cutoff was driven to shale, sufficient leakage occurred to develop high hydrostatic pressure at the downstream toe that produced a head of 45 ft above the

natural ground surface. This uplift pressure was first observed in piezometers

installed in the pervious foundation. The first surface evidence of the high

hydrostatic pressure came in the form of discharge from an old well casing that

had been left in place. Since it was important that the installation be made

as quickly as possible, 4- and 6-in. well casings, available at the site, were

slotted with a cutting torch and installed in the pervious stratum with solid

(riser) pipe extending to the surface. Wells were first spaced on 250-ft

centers and later intermediate wells were installed making the spacing 125 ft.

The hydrostatic pressure at the downstream toe was reduced from 45 to 5 ft and

the total flow from all wells averaged 10 cu ft per sec (U. S. Army Engineer

District, Omaha 1982). The first use of relief wells in the original design of

a dam was by the U. S. Army Engineer District, Vicksburg, when wells were

installed during construction of Arkabutla Dam, Mississippi, completed in June

1943. The foundation consisted of approximately 30 ft of impervious loess

underlain by a pervious stratum of sand and gravel. The relief wells were

installed to provide an added measure of safety with respect to uplift and

piping along the downstream toe of the embankment. The relief wells consisted

of 2-in. brass wellpoint screens 15 ft long attached to 2-in. galvanized

wrought iron riser pipes spaced at 25-ft intervals located along a line 100 ft

upstream of the downstream toe of the dam. The top of the well screens was

installed about 10 ft below the bottom of the impervious top stratum. The well

efficiency decreased over a 12-year period to about 25 percent primarily as a

result of clogging of the wells by influx of foundation materials into the

screens and/or the development of corrosion or incrustation. However, the

piezometric head along the downstream toe of the dam, including observations

made at a time when the spillway was in operation, has not been more than 1 ft

above the ground surface except at sta 190+00 where a maximum excess hydrostatic head of 9 ft was observed (U. S. Army Engineer Waterways Experiment

Station 1958). Since these early installations, relief wells have been used at

9-64
EM 1110-2-1901

30 Sep 86

many dams to prevent excessive uplift pressures and piping through the

foundation.

c. Design Considerations.

(1) General. The factors to be considered in determining the need for

and designing a relief well system include characteristics of the landside top

stratum; permeability, stratification, and depth of the pervious foundation in

which. seepage is to be controlled; net head acting on the dam; dimensions of

the relief well system being considered; allowable factor of safety with

respect to uplift at the downstream toe of the dam; and allowable rate of discharge through the pervious foundation. Some factors, like the net head acting on the dam, can be determined with good accuracy. Other factors like

permeability and stratification are more difficult to assess. The design of

the relief wells should be based on the best estimate of permeability values

and then subjected to a sensitivity analysis using several values of permeability to ensure that the adopted design is adequate to intercept seepage and

lower uplift pressures to the required extent allowing for the likelihood that

the values of permeability used in design lake precision (Kaufman 1976). The

area between the dam abutments is divided into reaches where geologic and soil

conditions are assumed uniform within the reach (see figure 9-24). Generally,

the design procedure for relief wells consists of determining the head which

would exist along the downstream toe of the dam without relief wells, comparing this head to that desired for a given factor of safety, and designing a

relief well system to reduce the head to the desired value. There is no

unique solution because there is an infinite number of well systems (radius,

penetration, spacing, etc.) which reduce the head to the given value. The

objective is to select one which is economical, has reasonable dimensions, and

can produce the desired results. Usually the designer selects the radius and

penetration and then determine the required spacing of the well system. This

becomes an iterative procedure wherein the designer assumes a value of well

spacing, computes the head between wells and repeats this for several trial

spacings until a spacing is found that produces the desired head along the

downstream toe of the dam. The cost of the well system is determined and then

a design can be prepared for a different penetration to determine if some

economy can be achieved by changing the penetration of the system. Fully penetrating relief wells are often used in aquifers up to about 75 ft thick. For

larger depths of pervious strata, it is usually more economical to have well

systems with 50 percent or greater penetration at closer spacing. The equations for relief well design depend upon the values of the source of seepage

and seepage exit length as shown in figure 9-25. The source of seepage is

assumed to be a line source parallel to the well system and the dam axis. The

location of the source of seepage depends upon the thickness and vertical

permeability of any natural top stratum upstream of the dam and any impervious

blanket constructed upstream of the dam, the permeability and thickness of the

pervious foundation, and the presence of any borrow pits and/or major erosion

features which reduce the thickness of the top stratum (see procedure to

evaluate the source of seepage given in U. S. Army Engineer Waterways Experiment Station 1956a). The value of the seepage exit (X3 in figure 9-25)

depends upon the thickness and permeability of the top stratum downstream from

the toe of the dam, the thickness and permeability of the pervious substratum,

9-65
EM 1110-2-1901

30 Sep 86

Figure 9-24. Profile of typical design reaches for relief

well analysis (prepared by WES)

and the presence of any geologic features and/or man-made features which would

result in an open or blocked seepage exit. The procedure for computation of

the seepage exit distance, rate of discharge through the pervious foundation

per unit length of dam, and pressure head without relief wells is given in

figure 9-26. Generally relief wells have diameters of 6 to 18 in. and screen

lengths of 20 to 100 ft, depending on the requirements. Some types of screens

used for wells are slotted or perforated steel pipe, perforated steel pipe

wrapped with steel wire, slotted wood stave pipe, and slotted plastic pipe.

Riser pipe usually consist of the same material as the screen but does not

contain slots or perforations. The open area of a well screen should be sufficiently large to maintain a low entrance velocity (< 0.1 ft per sec) at the

design flow in order to minimize head losses across the screen and reduce the

incrustation and corrosion rates. The entrance velocity is calculated by

dividing the expected or desired yield of the relief well by the area of openings in the screen (Johnson Division, Universal Oil Products Co. 1972). Filter packs around relief wells are usually 6 to 8 in. thick and must meet the

criteria specified in Appendix D. Head losses within the relief well system

consist of entrance head loss, friction head loss in the screen and riser

pipes, and velocity head loss as shown in figure 9-27. The effective well

radius is that radius which would exist if there were no hydraulic head loss

into the well. For a well without a filter, the effective well radius is

one-half the outside diameter of the well screen. Where a filter has been

placed around the well, the effective well radius is the outside radius of the

well screen plus one-half of the thickness of the filter.

9-66
EM 1110-2-1901

30 Sep 86

Figure 9-25. Design of relief wells (prepared by WES)

(2) Effective Well Penetration. In a stratified foundation, the effective well penetration usually differs from that computed from the ratio of the

length of well screen to the total thickness of the aquifer. The procedure

for determining the required length of well screen to achieve an effective

penetration in a stratified aquifer is as follows. Each stratum of the pervious foundation is first transformed into an isotropic layer (Leonards 1962)

where

d = transformed layer thickness

d' = actual layer thickness

kH = horizontal permeability of layer

kv = vertical permeability of layer

(9-24)

9-67
EM 1110-2-1901

30 Sep 86

Figure 9-26. Computation of rate of discharge and pressure heads for semipervious downstream top stratum and no relief wells (from U. S. Army

Engineer Waterways Experiment Station 120 )

9-68

Seepage per unit length of dam •••• Q 

s 

Head beneath top stratum of 

downstream toe of dam •.•.••.•.•••• h = 

0 

A factor •••••••••••••••••••••••••• c = 

CASE l, 1

3 

= ... 

x3 

1 X ., - 3 c 

h = h t-cx 

X 0 

(t = 2. 718) 

1 

= tanh(cL3 c ) 

cosh· c(L3 - x} 

h = h 

X 0 cosh(cL3 ) 

h 

h 0 

= (ct3 ) x=L3 cosh 

CASE 3, OPEN EXIT 

sinh c{L3 - x) 

hx = ho sinh (cL3

) 

hx=L 

3 

NOTE: x 1 can be COI:If·t:.ted ~r-on. formulas for x 1 by 

inserting the ~ength of upstrerum blanket L1 fO~ L 

in the appropn.ute exnressi<"'r, when upstrenm condl.tiods 

are similar to the above do~nstreP~ conditions. 

= 0 
9-69

fOTAL. HYDRAULIC HEAD LOSS IN A WELL (Hw) IS 

He ENTRANCE HEAD LOSS (SCREEN AND FILTER) 

ESTIMATE FROM CURVE a 

H HEAD LOSS IN SCREENED SECTION OF WELL 

' fSTIMATE FROM CURVE b FOR A DISTANCE OF ONEHI\LF THE SCREEN LENGTH 

H, L 055 WITHIN THE RISER AND CONNECTIONS. 

EST tMA 1 E FROM CURVE b 

H VELOCITY HEAD LOSS. ESTIMATE FROM CURVE c. 

v 

THL VAL.UE OF 11 MUST BE SUBTRACTED FROM THE COMPUTED 

V•\LUE OF- h"' TO OBTAIN THE LII"T OR WATER LEVEL IN A WELL. 

w 

u 

z 

<t 

Jr f-

';; "-LJj I 2,0 

z • 

W I 

wJr Ul 

.J 

u 

"7 {J t .0 

;;: " w 

rr r 

w 

f-

_j 

DEVELOPED FROM-----

PUMPING TEST 

DATA. 16-IN.-DIAM 

WELL,\00-SQ-IN SCREEN 

WITH 5/32-IN SLOTS, 

6-IN.·THICK FILTER 

Co ---J. -- - -- _j ____ ..L_ __ _j_ __ ..L_ _ _i __ .J.... __ __j __ ....l 

0 1C 20 30 40 so 

Wl:LL DISCHARGE PER FT OF SCREEN, GPM 

(a) 

Jr 

r" 

t- Jr 

"- 0 

Ul • 

"'I 0 

_j • 

w 

on. 

.. -

wn. 

I U. 

z 0 

Off="-

uo 

-0 

ll -

"-

f-

"-

..:: 

! 

"' "' 0 

_j 

0 

.. 

w 

I 

}-

1-

\0.0 

s.o 

3.0 

1.0 

0.5 0.3 

0.1 

u 0.05 0 

.J 

w 0.03 

> 

TYPE OF PIPE 

STEEL \NEW) STEEL IAVG CONDITION! 

WOOD STAVE RISER 

WOOD STAVE SCF<EEN 

CORRUGATED M£TAL 

c 

I ?5 

,, a· 

130 

100 

70 

10 100 1,000 

DISCHARGE, GPM 

O

00

10

BASED ON HAZEN-WILLIAMS EQUATION WITH C = 

LOSSES BY I \00/C)I.BS FOR VALUES OF C OTHE

(b) 

DISCHARGE, GPM 

(c) 

Figure 9-27. Hydraulic head loss in relief wells (after Leonards205 ) 
EM 1110-2-1901

30 Sep 86

The transformed permeability of each layer of the pervious foundation is

(9-25)

where is the transformed permeability of layer. The thickness of the

transformed, homogeneous, isotropic pervious foundation is

(9-26)

where D is the thickness of pervious foundation. The effective permeability

of the transformed pervious foundation is

(9-27)

where k is the effective permeability of transformed pervious foundation.

The effective well screen penetration into the transformed pervious foundation

is

where

w = effective well screen penetration into transformed pervious

foundation

= actual well screen length

(9-28)

The percent penetration of the well screen into the transformed pervious

foundation is

9-70
EM 1110-2-1901

30 Sep 86

(9-29)

where is the actual pervious foundation thickness.

(3) Factor of Safety. The factor of safety against uplift or heaving

at the downstream toe of the ham, based upon the critical gradient, is

(9-30)

where

Fh = factor of safety against uplift or heaving at the downstream toe

of the dam

iC R = critical upward hydraulic gradient under the top stratum at the

downstream toe of the dam

iO = allowable upward hydraulic gradient under the top stratum at the

downstream toe of the dam

= submerged unit weight of downstream top stratum soil

ha = allowable pressure head under the top stratum at the downstream

toe of the dam

Zb L = thickness of downstream top stratum

= unit weight of water

The factor of safety against uplift or heaving at the downstream toe of the dam

provided by the relief well system should be at least 1.5 (1)

.

(4) Infinite and Finite Relief Well Systems. Formulas for the design

of relief wells are based on the assumption that the flow is laminar,

(1) Relief wells should be designed to reduce the excess head to zero to prevent upward seepage from occurring beneath the downstream top stratum.

9-71
EM 1110-2-1901

30 Sep 86

artesian, and continuous and that a steady-state condition exists. Relief well

systems are considered to be infinite or finite in length. The term infinite

is applied to a system of wells that conforms approximately to the following

idealized conditions:

(a) The wells are equally spaced and identical in dimensions.

(b) The pervious foundation is of uniform depth and permeability along

the entire length of the system.

(c) The effective source of seepage and the effective line of

downstream exit are parallel to the line of wells.

(d) The boundaries at the ends of the relief wells are impervious,

normal to the line of wells, and at a distance equal to one-half the well

spacing beyond the end wells of the system.

If these conditions exist, the flow to each well and the pressure distribution

around each well are uniform for all wells along the line. Therefore, there

is no flow across planes centered between wells and normal to the line, hence

no overall longitudinal component of flow exists anywhere in the system. The

term infinite is applied to such a system because it may be analyzed mathematically by considering an infinite number of wells; the actual number of

wells in the system may be from one to infinity. Normally, a line of relief

wells below a dam extending entirely across a valley and terminating at relatively impervious valley walls should be designed as an infinite line. A

finite system of wells in any system that does not approximate the idealized

condition for the infinite system. Whenever a major and abrupt change in the

character of the system such as penetration or well spacing might result in

an appreciable component of flow parallel to the line of wells, the use of

design procedures for finite systems will be used (see U. S. Army Corps of

Engineers 1963).

(5) Drawdown to Infinite Line of Fully Penetrating Relief Wells with

Impervious Top Stratum. Where the flow to an infinite line of fully penetrating relief wells is from an infinite line source and the top stratum is

assumed to be completely impervious, (1) as shown in figure 9-28. The drawdown

produced by an equivalent continuous slot is

(9-31)

(1) Also applicable-when the top stratum is semipervious provided the well

system is located in a drainage ditch and the head is kept below the

ground surface on the downstream side of the dam to prevent any seepage

upward through the top stratum. Under these conditions, the downstream

top stratum acts as if it is impervious.

9-72
EM 1110-2-1901

30 Sep 86

where

H - he = drawdown produced by flow from continuous slot

Qw = discharge from equivalent continuous slot

L = distance from line source of seepage to wells

k = effective permeability of transformed pervious foundation

D = thickness of transformed pervious foundation

a = well spacing

However,

This head

an additional head occurs because of converging flow at the wells.

loss is a function of well flow, well spacing and penetration, well

radius, and thickness and permeability of the pervious foundation. For fully

penetrating wells

(9-32)

where

= head loss at well due to converging flow (see figure 9-28)

r w = effective radius of well (outside radius of well screen plus

one-half of the thickness of the filter)

The total drawdown at the well, neglecting hydraulic head losses in the well,

is that at the slot plus that due to the well

Substituting equations 9-31 and 9-32 into equation 9-33

(9-33)

(9-34)

9-73
EM 1110-2-1901

30 Sep 86

a. Plan view of wells

b. Section A-A c. Section B-B

Figure 9-28. Flow to an infinite line of fully penetrating

relief wells from an infinite line source of seepage (after

Leonards205)

The head midway between wells will exceed the head at the well by

(9-35)

where is the head increase midway between wells.

between wells is

The drawdown midway

(9-36)

At a distance downstream from the well system, the head will exceed that at

the well by

9-74
EM 1110-2-1901

30 Sep 86

where is the head increase downstream

of the wells is

of wells. The drawdown downstream

(9-37)

(9-38)

(6) Drawdown to Infinite Line of Partially Penetrating Relief Wells

with Impervious Top Stratum. For an infinite line of partially penetrating

relief wells where the flow is from an infinite line source and the top stratum

is assumed to be impervious (or semipervious as previously described) the head

loss at the partially penetrating well due to converging flow is

(9-39)

where is the average uplift factor (obtained from figure 9-29). The

total drawdown at the partially penetrating well, neglecting hydraulic head

losses in the well, is that at the slot plus that due to the well

(9-40)

The head midway between partially penetrating wells will exceed the head at

the well by

(9-41)

where

is the midpoint uplift factor (obtained from figure 9-29). The drawdown midway between partially penetrating wells is

(9-42)

9-75
9-76

• .!!. 

0 

iS 

2' 

Q 

.... 

"' "' .... 

w 

z 

w 

Q_ 

_J 

.J 

cJ 

.... 

2 

w 

<) 

a: 

w 

"-

t· 

I 

- -

\()0 

'!-0 

/!'l 

,o >---

·- I 

It 

l 

u ! 

,.;: 

t [ 

I .I II 

II j '1 j II 

/ 

-- -1 

Figure 9-29. 

relief wells 

a.lrw 

-

-

. 

' 

o.l 

-

0.5 

- -

I I 

- - -

i 

10 

I 

! - -- I 

I -- I 

- --

-- f-j E I > a> 

I , 41 > 

I a> " 

I 

---- -f- 20 

I 

2> 

-

- - - 3.0 

-

g g N 

qlr,. 

Nomograph for obtaining 

(from U.S. Army Engineer 

•" KEY 

EXAMPLE. 

Where Q /rw :100, I 0, 9'6-= 1.0 

E 

CD 

; 

Step 1.· Locate Sav: I 0 on ca/rw line a 100 and mark point 

Step 2. Locate 0 /Q = 1.0 on Ola. hne for 9av 

Step ·3 Place tr•onqle on obova point$ located by steps I o

Step 4 Slide tnonqle parallel to intttol position to po.nt 0/a : 1.00 

Step 5. Reod off value at 9m on a/rw l1ne = 100. em: 1.05 

Step 6. Slide tnongle parallel to 1nil!ol posttion to pole potnt on 

Step 7. Read off percent screen penetrotton = 46% on alrw ""10

uplift factors for design of partially 

120 Waterways Experiment Station ) 

pen
EM 1110-2-1901

30 Sep 86

(7) Drawdown to Infinite Line of Relief Wells with Semipervious Top

Stratum. Where the top stratum is semipervious, the need for relief wells is

evaluated by determining the piezometric grade line without relief wells using

blanket formulas given in figure 9-26. As stated previously, the factor of

safety against uplift or heaving at the downstream toe of the dam, as determined from equation 9-30, should be at least 1.5. If relief wells are

required, the spacing for an infinite line of relief wells for a given penetration is determined using a procedure of successive trials and the nomograph

given in figure 9-29. The required well spacing is affected by hydraulic head

losses in the well which are estimated from figure 9-27. The procedure for

computing the well spacing is as follows:

(a) Compute the allowable pressure head under the top stratum at the

downstream toe of the dam from

(9-43)

where

ha

= allowable pressure head under the top stratum at the downstream

toe of the dam

= submerged unit weight of downstream top stratum soil

Zb l = thickness of downstream top stratum

= unit weight of water

Fh = factor of safety against uplift or heaving at the downstream toe

of the dam

(b) Assume that the net head in the plane of the wells equals the

allowable pressure head under the top stratum at the downstream toe of the dam

and compute the net seepage gradient toward the well line

where

net seepage gradient toward the well line

h = net head acting on the dam

Havg = net head in the plane of the wells

9-77

(9-44)
EM 1110-2-1901

30 Sep 86

S = distance from line of relief wells to effective source of seepage

entry (see procedure in U. S. Army Engineer Waterways Experiment

Station 1956a)

X3

= distance from line of relief wells to effective seepage exit (see

procedure in figure 9-26)

Setting Havg = ha in equation 9-44 gives

(9-45)

(c) Assume a well spacing and compute the flow from a single well

where

(9-46)

Qw = flow from a single well

kf = effective permeability of transformed pervious foundation

D = transformed thickness of pervious foundation

a = well spacing

= average uplift factor (obtained from figure 9-29)

(d) Estimate the total hydraulic head loss in the well from

figure 9-27.

(e) Compute the net average head in the plane of wells above the total

head loss in the well including elevation head loss (see figure 9-25) from

(9-47)

where

havg

= net average head in the plane of wells above the total head loss

in the well including elevation head loss

9-78
EM 1110-2-1901

30 Sep 86

Havg= net head in the plane of wells

HW = total head loss in the well including elevation head loss

(f) Substitute values obtained from and havg from equation 9-45

and 9-47, respectively, and solve for the average uplift factor

(9-48)

where is the average uplift factor.

(g) Find from figure 9-29 using the values of a used in

equation 9-48 and the corresponding a/rw and D/a values.

(h) The first trial well spacing is that of value a for which

from step (f) equals from step (g).

(i) Find from figure 9-29 for the first trial well spacing and the

corresponding values of a/rw and D/a .

(j) If repeat steps (c) to (i) using the first trial well

spacing in lieu of the spacing originally used in step (c), and determine the

second trial well spacing. This procedure should be repeated until relatively

consistent values of a are obtained on two successive trials. Usually the

second trial spacing is sufficiently accurate.

If in step (j), a modified procedure is used for the second trial:

(k) Assume Hm = ha and compute QW from equation 9-46 using the

value of AM obtained in step (b) and the first trial well spacing from

step (h).

(1) Estimate Hw from Qw of step (k) and figure 9-27.

(m) Compute the net head beneath the top stratum midway between the

wells above the total head loss in the well including elevation head loss (see

figure 9-25) from

(9-49)

where

hm = net head beneath the top stratum midway between the wells above the

total head loss in the well including elevation head loss

9-79
EM 1110-2-1901

30 Sep 86

Hm

= net head beneath the top stratum midway between the wells

HW

= total head loss in the well including elevation head loss

h

(n) Using from steps (h) and (i), respectively, compute

avg from

(9-50)

where h avg

is the net head in the plane of wells.

(o) Using Hw and h from steps (1) and (n), respectively, and

compute H from

avg

avg

(9-51)

(p) Compute from equation 9-44 using Havg from step (o).

(q) Using hm and from steps (m) and (p), respectively, compute

for various values of a from

(9-52)

where is the midpoint uplift factor.

(r) Find from figure 9-29 for the values of a used in step (q)

and the corresponding a/r w and D/a values.

(s) The second trial well spacing is that value of a which from

step (q) equals from step (r).

(t) Find from figure 9-29 for the second trial well spacing and

the corresponding values of a/rw and D/a .

(u) Determine the third trial well spacing by repeating steps (k) to

(t) using the second trial well spacing in lieu of the spacing originally

assumed in step (k), and in step (n) using the values of and from

steps (s) and (t), respectively, instead of those from steps (h) and (i). This

procedure should be repeated until relatively consistent values of a are

obtained on two successive trials. Normally, the third trial is sufficiently

accurate.

9-80
EM 1110-2-1901

30 Sep 86

(8) Drawdown to Finite Line of Relief Wells. In a short, finite line of

relief wells, the heads midway between wells exceed those for an infinite line

of wells both at the center and near the ends of the well system as shown in

figure 9-30. Note that the pressures between wells, or midpoint pressures, are

lower at the center of the well system and gradually increase towards the end

of the line. With an infinite line of wells, the heads midway between wells

are constant along the entire length of the well line. Numerous well systems

may be fairly short, and for these it will be necessary to reduce the well

spacing computed for an infinite line of wells so that heads midway between

wells will not be more than the allowable pressure head under the top stratum

at the downstream toe of the dam. The ratio of the head midway wells at the

center of finite well systems to the head between wells in an infinite line of

wells, for various well spacings and seepage exit lengths, is given in

figure 9-31. The spacing of relief wells in a finite line should be the same

as that required in an infinite line of wells to reduce the head midway

between wells to ha divided by the ratio of 

I

from figure 9-31. In

any finite line of wells of constant penetration and spacing, the head midway

between wells near the ends of the system exceeds that at the center of the

system. Thus at the ends of both short and long well systems, the relief

wells should generally be made deeper to provide additional penetration of the

pervious substratum so as to obtain the same head reduction as in the central

part of the well line. The above-mentioned procedures for designing finite

relief well systems, although approximate, are usually sufficient. More exact,

but more complex, procedures are available (see U. S. Army Corps of Engineers

1963).

Figure 9-30. Variation of pressure relief along a finite line of relief

wells (after EM 1110-2-1905)

9-81
9-82

4.0 

:Lt"tl 

Q 

.... 

..{ 

IX' 

.!. 

1 50 

2 10() 

3 150 

4 200 

x3 

250 

500-

'500 

500 

Assumptions: 

Note: 

(1) Penetration of pervious aquifer by ve11 scre

{2) Semipervious top stratum infinite in landva

{3) Effective ve11 radius = 1.0 ft 

(l)H = Head midvay betveer. vells in infinite v

m 

... 

(2)Hm = Head midvay betveen vells at center of 

n vell line 

(3) a= Well specing in feet 

(4) x3 = Exit length in feet l.O 

200 400 600 800 1000 1200 I 

LENGTH Of WELL REACH IN fEET 

Figure 9-31. Ratio of head midway between relief wells at center of a finite wel

head midway between wells in an infinite system (from U.S. Army Engineer Waterway

s . 120) ment tat1on 
EM 1110-2-1901

30 Sep 86

d. Installation. While the specific materials used in the construction

of relief wells and methods of installation differ, relief wells are basically

very similar. They consist of a boring to facilitate the installation, a

screen or slotted pipe section to allow the entrance of ground water, a filter

to prevent entrance and ultimate loss of foundation material, a riser pipe to

conduct the water to the ground surface, a check valve to prevent backflooding

and entrance of foreign material detrimental to the installation, backfill to

prevent recharge of the formation by surface water, a bottom plug to prevent

inflow of soil, (1) a V-notch weir at the top of the relief well to facilitate

measurement of flow, and a cover and some type of barricade protection to prevent vandalism and damage to the top of the well by maintenance crews, livestock, etc. (see figure 9-23). Following development of the relief well, a

pumping test should be conducted to determine the specific yield of the well

and the amount of sand infiltration. Information from the pumping test is

used to determine the acceptability of the well and for evaluating any changes

in performance or loss of efficiency with time. Procedures for installation,

development, and pumping tests are given in EM 1110-2-1913. A guide specification for relief wells is available.

e. Monitoring. As mentioned previously, the discharge of relief wells

gradually decreases with time due to clogging of the well screen and/or reservoir siltation. Piezometers should be installed between relief wells to

determine the seepage pressure in the main pervious strata. Relief wells

should be sounded for sand and pumped to determine their discharge capacity

under varying reservoir levels (see Chapter 13). A trend toward fall in

relief well discharge accompanied by a fall in piezometric levels indicates a

decrease in underseepage due to reservoir siltation and is favorable. However, a decrease in relief well discharge accompanied by a rise in piezometric

levels indicates clogging of the relief wells and immediate rehabilitation

and/or replacement of the wells or installation of additional wells is

required (Singh and Sharma 1976). The operation, maintenance, and rehabilitation of relief wells is discussed in Chapter 14.

9-8. Trench Drain.

a. Introduction. When a complete cutoff is not required or is too

costly, a trench drain may be used in conjunction with other underseepage control measures (upstream impervious blanket and/or relief wells) to control

underseepage. A trench drain is a trench generally containing a perforated

collector pipe and backfilled with filter material (see figure 9-32). Trench

drains are applicable where the top stratum is thin and the pervious foundation is shallow so that the trench can penetrate into the aquifer. The existence of moderately impervious strata or even stratified fine sands between the

bottom of the trench drain and the underlying main sand aquifer will render

the trench drain ineffective. Where the pervious foundation is deep, a trench

drain of practical depth would only attract a small portion of underseepage,

and detrimental underseepage would bypass the drain and emerge downstream of

the drain, thereby defeating its purpose. Trench drains may be used in

(1) For partially penetrating relief wells, the bottom plug should be such

that future screen extension will be possible,

9-83
EM 1110-2-1901

30 Sep 86

conjunction with relief well systems to collect seepage in the upper pervious

foundation that the deeper relief wells do not drain. If the volume of seepage

is sufficiently large, the trench drain is provided with a perforated pipe. A

trench drain with a collector pipe also provides a means of measuring seepage

quantities and of detecting the location of any excessive seepage (U. S. Army

Engineer Waterways Experiment Station 1956a, EM 1110-2-1911, EM 1110-2-1913,

and Cedergren 1977). 

b. Location and Geometry. Trench drains are generally located at the

downstream toe of the dam as shown in figures 9-32a and 9-32c, but are sometimes located beneath the downstream slope of the dam as shown in figure 9-32b.

Trench geometry will depend on the volume of expected underseepage, desired

reduction in uplift pressure, construction practicalities, and the stability of

the material in which the trench is to be excavated. Trenches with widths as

small as 2 to 6 ft have been used. However, narrow trench widths require

special compaction equipment (EM 1110-2-1913).

c. Design Considerations. The maximum head at the base of an impervious top stratum downstream of a toe trench drain overlying a homogeneous,

isotropic, pervious foundation may be computed from figure 9-33. The distance

to the source of seepage may be evaluated using the procedure given in U. S.

Army Engineer Waterways Experiment Station 1956a. If the pervious foundation

is stratified, it is transformed into an isotropic layer, as described previously (see Equations 9-24 to 9-27) prior to using figure 9-33. The' factor of

safety against uplift or heaving at downstream toe of the dam provided by the

trench drain should be at least 1.5. If the downstream top stratum is semipervious, seepage into the trench, and the maximum head landward of the

trench, will be somewhat less than that computed from figure 9-33 giving a

slightly conservative design. When there is no downstream top stratum, seepage flow into the trench can be estimated from a flow net analysis (U. S. Army

Engineer Waterways Experiment Station 1956a).

d. Construction. A trench drain usually contains a perforated pipe,

surrounded by filter gravel, and backfilled with sand as shown in figure 9-34.

Materials in trench drain must satisfy the filter gradation criteria given in

Appendix D. As filter materials are placed, they must be protected from

contamination resulting from inwash that might occur during a rainfall. The

same control procedures are used for trench drains as those used in construction of pervious fill in the main embankment (EM 1110-2-1911).

9-9. Concrete Galleries. Internal reinforced concrete galleries have been

used in earth and rockfill dams built in Europe, for grouting drainage, and

monitoring of behavior. Galleries have not been constructed in embankment

dams built by the Corps of Engineers to date. Some possible benefits to be

obtained from the use of galleries in earth and rockfill dams are as follows

(Sherard et al. 1963):

a. Construction of the embankment can be carried out independently of

the grouting schedule.

9-84
EM 1110-2-1901

30 Sep 86

a. Trench drain at downstream toe of dam

b. Trench drain under downstream slope of dam

c. Trench drain used in conjunction with relief wells

Figure 9-32. Trench drains to control underseepage (from

EM 1110-2-1913)

9-85
EM 1110-2-1901

30 Sep 86

Figure 9-33. Design of toe trench drains for homogeneous, isotropic,

pervious foundation, and for an impervious downstream top stratum

(from U. S. Army Engineer Waterways Experiment Station 120 )

b. Drain holes drilled in the rock foundation downstream from the grout

curtain can be discharged into the gallery and observations of the quantities

of seepage in these drain holes will indicate where foundation leaks are

occurring.

c. Galleries provide access to the foundation during and after reservoir

filling so that additional grouting or drainage can be installed, if required,

and the results evaluated from direct observations.

d. The additional weight of the overlying embankment allows higher

grout pressures to be used.

e. Galleries can be used to house embankment and foundation instrumentation outlets in a more convenient fashion than running them to the downstream toe of the dam.

f. If the gallery is constructed in the form of a tunnel below the rock

surface along the longitudinal axis of the dam, it serves as an exploratory

tunnel for the rock foundation.

9-86
EM 1110-2-1901

30 Sep 86

Figure 9-34. Trench drain with collector

pipe (from EM 1110-2-1913)

The minimum size cross section recommended for galleries and access shafts is 8

by 8 ft to accommodate drilling and grouting equipment. A gutter located along

the upstream wall of the gallery along the line of grout holes will carry away

cuttings from the drilling operation and waste grout from the grouting operation. A gutter and system of weirs located along the downstream wall of the

gallery will allow for determination of separate flow rates for foundation

drains (EM 1110-2-3502, and Blind 1982).

9-87
EM 1110-2-1901

30 Sep 86

CHAPTER 10

SEEPAGE CONTROL THROUGH EARTH ABUTMENTS ADJACENT TO STRUCTURES

AND BENEATH SPILLWAYS AND STILLING BASINS

10-1. Through Earth Abutments. Earth and rock-fill dams, particularly in

glaciated regions, may have pervious material, resulting from filling of the

preglacial valley with alluvial or morainal deposits followed by the downcutting of the stream, in one or both abutments (Twelker 1957). Seepage

through the pervious abutment(s) is combined with through seepage and underseepage to determine the total seepage loss. As mentioned previously, the purpose of the project, i.e., long-term storage, flood control, hydropower, etc.,

will determine the allowable seepage loss. Seepage control through earth

abutments is provided by extending the upstream impervious blanket in the

lateral direction to wrap around the abutment up to the maximum water surface

elevation, by placing a filter layer between the pervious abutment and the dam

downstream of the impervious core section, and, if necessary, by installing

relief wells at the downstream toe of the pervious abutment. At the North

Branch of Kokosing Dam, Ohio, the left abutment is an outwash terrace consisting of sands and gravels with layers of silt and clay as shown in figure 10-1.

Seepage control through the pervious abutment was provided by a 5-ft-thick

impervious upstream blanket which wrapped around the left abutment, a filter

layer between the pervious abutment and the dam downstream of the impervious

core (see figure 10-2), and three fully penetrating relief wells at the downstream toe of the pervious abutment (U. S. Army Engineer District, Huntington

1969).

10-2. Adjacent to Outlet Conduits. When the dam foundation consists of compressible soils, the outlet works tower and conduit should be founded upon or

in stronger abutment soils or rock. When conduits are laid in excavated

trenches in soil foundations, concrete seepage cutoff collars shall not be

provided solely for the purpose of increasing seepage resistance since their

presence often results in poorly compacted backfill around the conduit. Collars, with a minimum projection from the conduit surface, will be used over

conduit joints to protect against joint displacements resulting from differential movement on yielding foundations. Excavations for outlet conduits in

soil foundations shall be wide enough to allow for backfill compaction

parallel to the conduit using heavy rolling compaction equipment. Equipment

used to compact along the conduit should be free of framing that prevents its

load transferring wheels or drum from working against the structure. Excavated

slopes in soil for conduits should be no steeper than 1V to 2H to facilitate

adequate compaction and bonding of backfill with the sides of the excavation.

Drainage layers should be provided around the conduit in the downstream zone of

embankments without pervious shells. A concrete plug shall be used as backfill

in rock cuts for cut-and-cover conduits within the core zone to ensure a watertight bond between the conduit and vertical rock surfaces. The plug, which can

be constructed of lean concrete, should be at least 50 ft long and extend up to

the original rock surface. In embankments having a random or an impervious

downstream shell, horizontal drainage layers should be placed along the sides

and over the top of conduits downstream of the impervious core. Where outlet

structures are to be located in active seismic areas, special attention must be

given to the possibility of movement along-existing or possibly new faults

(EM 1110-2-2300).

10-1
10-2

EL. 1169 TOP Of DAM 

----------------------------------

[ 

--------c------

L ASSUMED SEEPAGE END SEEPAGE CUTOff I I CHANNEL LIMITS SANDS & 

GRAVELS\ 

----------t------

T1LL"\. 

25+00 ' 15+00 

Figure 10-1. Profile of left pervious abutment at North Branch of Kokosing Da

87 (from U. S. Army Engineer District, Huntington ) 
EM 1110-2-1901

30 Sep 86

Figure 10-2. Seepage control of left pervious abutment at North Branch

of Kokosing Dam, Ohio (from U.S. Army Engineer District, Huntington87 )

10-3. Beneath Spillways and Stilling Basins. Adequate drainage should be

provided under floor slabs for spillways and stilling basins to reduce uplift

pressures. For soil foundations, a drainage blanket under the slab with

transverse perforated pipe drains discharging through the walls or floor is

generally provided, supplemented in the case of stratified foundations by deep

well systems. Usually drainage of a slab on rock is accomplished by drain

holes drilled in the rock with formed holes or pipes through the slab. The

drainage blanket is designed to convey the seepage quickly and effectively to

the transverse collector drains. It is designed as a graded reverse filter

with coarse stones adjacent to the perforated drain pipe and finer material

adjacent to the concrete structure to prevent the migration of fines into the

drains. Outlets for transverse drains in the spillway chute discharge through

the walls or floor at as low an elevation as practical to obtain maximum pressure reduction. Wall outlets should be 1 ft minimum above the floor to prevent blocking by debris. Cutoffs are provided at each transverse collector

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pipe to minimize buildup of head in case of malfunction of the pipe drain.

Drains should be at least 6 in. in diameter and have at least two outlets to

minimize the chance of plugging. Outlets should be provided with flat-type

check valves to prevent surging and the entrance of foreign matter in the

drainage system. For the stilling basin floor slab, it may be advantageous to

place a connecting header along each wall and discharge all slab drainage into

the stilling basin just upstream from the hydraulic jump at the lowest practical elevation, in order to secure the maximum reduction of uplift for the

downstream portion of the slab. A closer spacing of drains is usually

required than in the spillway chute because of greater head and considerable

difference in water depth in a short distance through the hydraulic jump.

Piezometers should be installed in the drainage blanket and deeper strata, if

necessary, to monitor the performance of the drainage systems. If the drains

or wells become plugged or otherwise noneffective, uplift pressures will

increase which could adversely affect the stability of the structure

(EM 1110-2-2400 and EM 1110-2-2300).

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CHAPTER 11

SEEPAGE CONTROL IN ROCK FOUNDATIONS AND ABUTMENTS

11-1. General Considerations.

a. The choice of seepage control methods to use in rock foundations and

abutments is dependent on a number of factors. Characterization of the foundation or abutment and identification of potential seepage paths is essential.

Before any method of seepage control is implemented, the area must be

thoroughly explored and tested to assure that the method chosen will apply to

the general conditions as well as the conditions locally encountered and will

serve the intended purpose. In many cases, a combination of methods can be

used to the best advantage for rock foundations or abutments. The use of different control methods becomes particularly important when there is a change in

the character of the foundation from one location to another, or a change in

seepage characteristics between the foundation and the abutment.

b. Seepage should be cut off or controlled by drainage whenever economically possible. Safety, however, must be the governing factor for selecting a

seepage control method. It should be noted that the possibility exists for

control measures to cause substantial increases in seepage rather than

decreases. Such increases are normally accompanied by reductions in uplift

pressures and are therefore desirable if the increased seepage produces no

detrimental side effects. In the final choice of a seepage control method, or

methods, economic factors must be recognized and evaluated.

11-2. Cutoff Trenches.

a. No cutoff is 100 percent impervious and therefore the reduction in

seepage from cutoff trenches is a relative matter. Cutoff trenches are normally employed where the character of the foundation is such that the construction of a satisfactory or effective grout curtain is not practical. Such

trenches, when constructed, are normally backfilled with compacted impervious

material, bentonite slurry, or neat cement.

b. Construction of trenches in rock foundations and abutments normally

involves blasting using the presplit method with primary holes deck-loaded

according to actual foundation conditions. After blasting, excavation is normally accomplished with a backhoe. Cutoff of seepage within the foundation is

obtained by connecting an impervious portion of the foundation to the impervious portion of the structure by backfilling the trench with an impervious

material. In rock foundations, as in earth foundations, the impervious layer

of the foundation, in some cases, may be sandwiched between an upper and a

lower pervious layer, and a cutoff to such as impervious layer would reduce

seepage only through the upper pervious layer. However, where the thicknesses

of the impervious and upper pervious are sufficient, the layers may be able to

resist the upward seepage pressures existing in the lower pervious layer and

thus remain stable. Cutoff of seepage within the abutment is normally

obtained by extending the cutoff from above the projected seepage line to an

impervious layer within the abutment. The type of backfill material is normally dictated by condition of the foundation or abutment, economics, and

degree of cutoff required.

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11-3. Abutment Impervious Blankets.

a. Impervious blankets overlying the upstream or riverside face of pervious abutments, or foundations, are effective in reducing the quantity of

seepage and to some extent will reduce uplift pressures and gradients downstream. An impervious blanket may be used for earthen or rock abutments;

however, a filter material is normally required with rock abutments.

b. The construction of impervious blankets is particularly adaptable to

treating exposed pervious areas of abutments which are adjacent to the main

structure. In cases where a natural impervious blanket exists on the abutment,

ranging in depth from a few feet to many feet, full advantage should be taken

of the existing material. Upstream borrow along the abutment should be controlled to prevent excessive excavation of the natural impervious top blanket.

Conversely, localized areas which are thin and weak should be reinforced by

the addition of additional impervious material.

c. Blankets may sometimes give adequate control of seepage water for low

head structures, but for high head structures it is usually necessary to incorporate a downstream drainage system as a part of the overall seepage-control

design. The benefits derived from abutment impervious blankets are due to the

dissipation of a part of the reservoir head through the blanket. The proportion of head dissipated is dependent upon the thickness, length, and effective

permeability of the blanket in relation to the permeability of the adjacent

soil, or rock.

11-4. Drainage and Grouting Galleries and Tunnels.

a. Foundation galleries and tunnels in concrete gravity dams provide an

exit for foundation drains and convenient facilities for rehabilitation work,

or supplemental grouting, if required. The depth of drainage galleries, or

exit elevation of the drains, with respect to the tailwater, controls the

uplift downstream of the drains or wells. Generally, the lower the elevation

of the gallery, the more reduction in head, or uplift, is experienced. If the

depth of the drainage gallery is located and the gallery discharges at the

elevation of the tailwater, the magnitude of the uplift downstream of the wells

is normally very modest. The uplift, however, is controlled by well spacing,

well efficiency, and other seepage control measures, such as grout curtains and

cutoffs, in addition to the elevation of the drainage gallery and the elevation

at which it discharges. In special cases where the drainage gallery is very

deep, i.e., below tailwater, it is possible to actually create a negative uplift on the base of a dam. In such cases some of the seepage pumped from the

drainage gallery flows through the foundation to the drains from downstream.

b. Grouting curtains are frequently centered along drainage galleries or

tunnels. Remedial or supplemental' grouting may be performed from within

drainage tunnels. The additional grouting may be performed vertically or in

inclined, or sloping, boreholes. Also, should excessive uplift pressures

become evident, additional grouting to widen or deepen the curtain may be

performed or additional drainage wells may be installed from the gallery to

relieve excess pressures.

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11-5. Grouting of Foundations and Abutments.

a. The Corps‘ grouting methods have become less standardized in recent

years (Albritton, Jackson, and Banget 1984). Typically, however, a combination

of a line of drainage holes and a grout curtain provide an efficient and effective seepage control method. A properly installed grout curtain in the foundation of a structure not only provides a substantial reduction in seepage but

also reduces the uplift pressures downstream of the curtain. Conveniently, for

the great majority of dam sites, irrespective of type of rock, strike and dip

of strata, and faulting conditions, the pervious zone which requires seepage

control is relatively shallow and lends itself readily to control by grouting.

A comprehensive coverage of drilling methods, as well as grouting methods, is

presented in EM 1110-2-3506.

b. Grouting operations in foundations and abutments are not limited to

construction of grout curtains. Grouting may be used for foundation repair and

filling cavities or voids in limestone or carbonate formations. The requirement for a single- or multiple-line grout curtain is dictated by the condition

and integrity of the foundation as determined from preconstruction exploration.

c. Grouting of steep abutment slopes has the potential for causing difficulties and possibly can do more harm than good. Care must be exercised when

grouting in abutments to avoid displacements within the rock mass. Even relative low grouting pressures can cause joint opening and decrease the integrity

of the abutment.

d. In general the efficiency of a grouting operation for controlling

seepage in well graded sediments is proportional to the width of the curtain.

In rock foundations and abutments the seepage control accomplished by grouting

is not a function of width, however, but is dictated by the effectiveness of

sealing seepage paths and open joints identified in the exploration program.

The effectiveness of a grouting operation may be evaluated by pre- and postgrouting pressure injection tests for evaluating the water take and the foundation or abutment permeability.

11-6. Surface Treatment of Foundations and Abutments.

a. Surface treatment of foundations and abutments is essential to ensure

intimate contact of backfill materials with sound rock. Once a foundation is

exposed by excavation, the method of treatment and potential protection against

piping of embankment or abutment materials will be dictated by the conditions

encountered. All cavities, or caves, should be cleaned and plugged with concrete, both upstream and downstream from the core trench. All openings, fissures, joints, etc., should be cleaned after excavation and treated with dental

concrete, where possible. Treatment with dental concrete stops major deterioration of materials that weather rapidly during construction, and helps to

prevent lateral piping of the embankment material into the adjacent foundation.

b. If a well-developed, highly solutioned joint system, or similar condition is encountered in the abutment, thick concrete walls may be placed

against the abutment. Prior to placement of concrete walls the abutment face

must be set back and cleaned, with presplitting being occasionally required.

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Concrete walls offer the advantage of either filling or blocking cavities,

affording a reasonable condition for treatment by grouting, and provide an

abutment "tie-in" for fill placement with ideal conditions for maximum compaction of the adjacent embankment.

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CHAPTER 12

REMEDIAL SEEPAGE CONTROL

12-1. General Considerations. This chapter assumes that a seepage problem

with an existing structure has been identified and defined by methods discussed in Chapter 13, or by other observations. The next step is to decide on

a remedy, design and install the remedial measure, and monitor its performance

to determine if the problem has been satisfactorily addressed. Several factors, including consequences of continued detrimental seepage, the geotechnical

environment (embankment, foundation, abutment), and economy, will determine the

type and degree of remedial seepage control. Some of the more critical consequences include:

a. Breaching of the embankment or loss of support to structural members

due to piping.

b. Breaching of the embankment from slope instability induced by loss of

material and/or strength due to seepage.

c. Loss of significant amounts of reservoir water.

d. Maintenance problems or loss of useful areas due to seepage on the

downstream slope or areas downstream of the embankment.

12-2. Remedial Methods.

a. Factors Affecting Choice of Methods, Several methods of reducing

undesirable seepage are discussed in this chapter; most have been previously

addressed in Chapters 8-11, which described methods and appropriate settings

for each. The remedial designer, while possibly having more advanced technology available than the original designer, must work with existing conditions.

The embankment and its foundation, abutments, and seepage control measures may

form a complicated structure through which seepage occurs. This can make precise detection and remedial control difficult or impossible. Remedial action

may range from continued or additional monitoring to rebuilding or abandonment

of the dam. Choice of remedial method(s) will depend on several factors, which

include:

(1) Geotechnical environment.

(2) Risk.

(3) Degree of correction required.

(4) cost.

b. Effects of Methods on Other Structure Elements. The remedial

designer must also consider the interplay of the remedial measures with other

dam elements. For example:

(1) Effect of excavation for drains, cutoff trenches, slurry trenches,

etc., on embankment stability.

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(2) Difficulty of tying remedial measure to existing seepage control

elements.

(3) Possibility of hydraulic fracturing when grouting.

c. Monitoring. In all cases, pre- and post-remedial monitoring of seepage is essential to determine the effectiveness of remedial action. Since

Chapters 8-11 describe control measures in detail, this chapter will just point

out primary considerations in the choice of remedial measures and give examples

of their use. These examples are provided for general guidance only, since

efficient use of remedial measures is very dependent upon geotechnical characteristics of the particular site's as-built configuration, reservoir uses, and

pool history.

12-3. Storage Restriction. The most direct method to alleviate a seepage

problem is to lower the reservoir and restrict pool levels in order to stop or

reduce seepage and its effects. This is often done during problem identification. If piezometer and seepage quantity measurement devices are in place at

this time, the effect of this remedy will be experimentally determined.

Considerations in storage reduction include:

a. Reduction of downstream inundation area and level should breaching

occur.

b. Effects of pool lowering on water supply, flood control, power generation, navigation, recreation, and environment.

Normally, lowering and restriction of the reservoir pool is not an acceptable

long-term solution, but this depends on restriction levels and purpose of the

reservoir. Care must be taken in lowering the reservoir since rapid drawdown

can lead to instability of the upstream slope. Of course, risk of upstream

slope failure would normally be a preferred alternative to breaching of the dam

and release of a full reservoir.

12-4. Grouting. Grouting is a common, long-used remedy for seepage. Its

effectiveness is dependent upon being able to rather specifically locate the

leaking area and fill the culprit openings without damage to the embankment.

Possible damage includes cracking of impermeable cores or other impermeable

areas of the embankment, foundation, or abutments, and clogging of drains. If

grouting results in sealing of the foundation just downstream of or beneath the

downstream portion of the dam, uplift pressures may increase beneath the

embankment or seepage may be forced up into the downstream portion of the

embankment. Pore pressure instrumentation should be in place to monitor such

changes before grouting begins. This must be considered in design of remedial

controls. Because of the many variables in grouting, it is highly desirable

to have an experienced contractor and field engineer. In many cases, postgrout drilling may be warranted to determine if the grout has thoroughly penetrated the desired area. Information about grout properties and grouting is

given in Chapters 9 and 11. Several case histories follow which provide

general examples.

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a. 95-ft-High Earthfill Dam (Ley 1974). Upon initial filling, an earthfill dam with a foundation and abutments of volcanic tuffs and breccias exhibited leakage at one of the downstream embankment-abutment contacts and out onto

the downstream slope. Inspection revealed leakage from open fractures in the

volcanic rock and drains were installed in the areas of seepage. The seepage

was stable for a number of years. Subsequent evaluation of the embankment for

seismic safety resulted in a need to reduce foundation seepage quantities and

piezometric levels within the embankment. A grouting program employed a low

viscosity chemical grout in order to penetrate any permeable layers in the

embankment where seepage might be occurring. Grout holes were split-spaced for

120 ft along the dam crest from the left abutment. If significant circulation

water was lost during drilling, the hole was grouted. Initial spacing was

12 ft with 14 of 23 holes taking low pressure grout (0-5 psi at the collar of

the hole). This low pressure was to prevent embankment heave. Most of the

take was well into the left abutment with holes spaced as close as 2-1/2 ft and

being deepened in stages and further grouted. Gel time varied from 2 to

18 minutes and final depth of holes varied from 24 to 84 ft. Total take was

3,200 gal with seepage being reduced 90 percent, but with little reduction in

piezometric levels. Grouting can reduce seepage quantities significantly but

still not alleviate high piezometric pressures, particularly in tight or finegrained materials since any continuous void or pore space can transmit upstream

heads.

b. 140-ft-High Earth Dam (Ley 1974). In the left abutment, gypsum had

apparently formed in the bedding planes and fractures of folded and faulted

shale and siltstone. After water was impounded, leakage, carrying dissolved

gypsum, occurred from the abutment. Settlement and gradual increase in seepage also indicated that gypsum was being removed from the formation. Built in

1915, the dam underwent a grouting program from 1930-1933, resulting in placement of about 35,000 cu ft of grout in a series of holes along the dam crest,

the left abutment, and at the bottom of the hill forming the left abutment.

This program reduced seepage quantities by 75 percent. Approximately 30 years

later, over 32,000 cu ft of cement-bentonite grout (colored with iron oxide to

distinguish from previously placed grout) was placed in 137 holes to again

reduce seepage and replace material removed by solution. Cores indicated good

penetration with most seams from hairline to 1/8 in. thick. Seepage was

greatly reduced. Other geologic materials may also be dissolved when subjected

to seepage. In a similar manner, silt and clay in limestone cavities may also

be removed by seepage. Grouting may only be a temporary solution to a seepage

problem if solution of a soluble foundation continues after grouting.

c. 70-ft-High Earthfill Dam (Ley 1974). Seepage of 130-140 gal/minute

was discovered downstream and attributed to foundation leakage. Installation

of drains downstream of the dam allowed collection, metering, and return of

water to the reservoir. Drilling for a grouting program, undertaken some years

later to reduce seepage losses, revealed loose, sugarlike, decomposed granite

30-40 ft below the dam foundation. The grouting was unsuccessful in reducing

seepage. Subsequently, the bottom and right side of the reservoir were

covered with an impervious blanket of 40 tons of bentonite mixed with native

material. After mixing of the bentonite with native soil to a depth of 3 in.,

the surface was rolled with a rubber-tired roller. Surface drainage provisions

prevented runoff from eroding the blanket during partial pool. Seepage, after

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blanketing, decreased 50 percent. In this case, attacking the seepage problem

further upstream (at the reservoir) proved more efficient than trying to seal

an underlying seepage path.

d. Fontenelle Dam (Gebhart 1974). A 165-ft zoned embankment, Fontenelle

Dam, almost failed when a leak of up to 20 cu ft/second developed at the downstream contact with the right abutment. Much of the embankment was eroded

before drawdown was effective in stabilizing the embankment. Fortunately, outlet capacity allowed lowering the reservoir 3-4 ft per day. The source of

leakage was not specifically determined, but an extensive grouting of foundation rock (calcareous sandstone, siltstone, and carbonaceous shale) was successful in preventing a recurrence of the problem. A 90- by 140-ft cement

grout blanket was placed upstream from the original grout cap. Grout curtains

were extended beneath the dam beyond the abutments. Over 200,000 cu ft of

grout was used.

e. Hills Creek Dam (Jenkins and Bankofier 1972). Hills Creek Dam, constructed by the Portland District, has a maximum height of 338 ft and consists

of a central impervious core with gravel and rock shells. Minor seepage occurred near the left abutment during first filling, but decreased with time.

Seepage markedly increased in extent and volume after 6 years of normal operation. Vertical drains placed in the downstream shell as an initial remedial

measure were not effective in lowering water levels in the downstream shell and

seepage continued to increase. An investigation to determine the seepage

source continued during the remedial action. Initially it was thought that

leakage was through the upstream blanket into the foundation and abutment, but

further observations indicated flow was through the core or core-foundation

contact. Grouting , which injected 4,500 sacks of cement, most in a 1-1/2:1 mix

at zero psi, resulted in elimination of almost all seepage. Four 42-in. bucket

auger holes, as well as several smaller borings, were drilled to inspect

grouting of the core and foundation. The main source of seepage was at a point

along the core foundation contact where a haul road had crossed the abutment.

Twelve years later, seepage is still negligible. Frequently, the source of

seepage is not obvious. The engineer must consider all possibilities and,

after choosing and installing a remedial measure, try to understand what postremedial monitoring is indicating. The extent of the engineer's knowledge of

the foundation, embankment materials, and construction history will greatly

influence the accuracy of his analysis of the seepage problem. Often available

foundation and construction information will not be adequate and further

geotechnical investigation will be required.

12-5. Upstream Impervious Blanket.

a. If it is determined that sealing of the reservoir bottom and sides

immediately upstream of the embankment will be useful in reducing undesirable

seepage quantities and pressures beneath the embankment, an upstream impervious

blanket may be employed. If successful and economically feasible, this is one

of the most efficient measures since the source of water, the reservoir, is

controlled upstream of the embankment and its foundation. This generally

requires removal of reservoir water, though some small reservoirs have been

sealed by placement of materials through water. Sources of fine-grained material and, in some cases, filter materials are required. The impervious

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materials are usually placed on the reservoir bottom. If sloped areas such as

the reservoir sides of upstream embankment slope are to be sealed, consideration must be given to protection against wave attack and erosion from runoff.

Additionally, fine-grained materials placed on the upstream embankment slope

may be removed during drawdown because of low saturated strength and high

saturated weight. If seepage can also go through the upstream portion of the

embankment and then into the foundation an upstream blanket will be less effective and another remedy may be necessary, e.g., cutoff beneath dam, figure 12-1. The nature of reservoir bottom materials must be considered. Any

large voids must be filled with a stable material such as compacted soil,

Figure 12-1. Possible problem if existing and remedial seepage

control measures are not properly coordinated (prepared by WES)

stabilized soil, concrete etc. High gradients will likely exist through the

blanket during high reservoir levels, particularly close to the embankment. It

may be necessary to place a filter material before placing the blanket to prevent piping of the blanket material into the foundation. The extent of the

blanket is determined by analysis and will depend on several factors, including

extent of desired decrease in seepage quantities and pressures and blanket

material available (quantity and permeability) (EM 1110-2-1913 and Barron

1977). Man-made liners have provided a seal for reservoirs with pervious

foundations when fine-grained materials were not economically available. They

are usually rather expensive, require relatively smooth surface for placement,

and coverings (normally soil) to protect them from puncture in stressed areas

and deteriorating exposure to sunlight. Joining of sections is one of the most

critical and difficult aspects of man-made liners. Field seams, especially

under difficult field conditions and with other than highly experienced personnel, can be an appreciable source of leakage. Quality control of seaming

should be strict. One example of the use of an impervious upstream blanket was

given in paragraph 12-3c; another is provided below:

b. An impervious upstream blanket connected to a sloping impervious core

was placed during the construction of Tarbela Dam on the Indus River in

Pakistan (Lowe 1978). The blanket material consisted of sandy silt mixed with

a sandy silt angular boulder gravel. The blanket lay over an alluvium of

cobble gravel choked with fine sand. The blanket, which was to increase the

length of seepage path and not necessarily to reduce seepage quantities, met

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the piping criteria, D15 (alluvium) < 5D85 (blanket), Appendix D. As the

reservoir emptied after first filling, several sinkholes and cracks were noted

in the blanket. Sinkholes ranged from 1 to 15 ft in diameter and 4 to 6 ft in

depth. It was felt that uneven settlement during the first reservoir filling

caused tension and compression cracks in the blanket which allowed considerable

seepage into the underlying sand-choked gravel. In areas where the sand was

less dense, the seepage moved the sand down to form a layer in the lower part

of the gravel. This created open work gravel just beneath the blanket, and

fines from the blanket moved into and through this open layer forming the sinkholes. Sinkholes were filled with filter material and mounded over with

blanket material. Typically, the blanket mounds were approximately 15 ft high

and extended 30 to 35 ft beyond the sinkhole edge. After filling of the reservoir, sinkholes were located by side-scan sonar and filled with a mixture of

filter material and silt from self-propelled bottom dump barges. Each sinkhole

generally received 50 barge loads of material. Sinkholes continued to be discovered and covered over another 3-4 years after the initial remedial action.

Siltation on the reservoir blanket and filling of sinkholes have reduced

seepage about one half.

12-6. Downstream Berm. Berms control seepage by increasing the weight of the

top stratum so that the weight of the berm plus top stratum is sufficient to

resist uplift pressure. If of low permeability, they will reduce seepage, but

increase uplift pressures beneath the downstream toe of the dam since they

force seepage to exit further downstream of the dam. If pervious, they must

be designed as a filter or with an underlying filter to prevent upward migration of line particles from the foundation materials beneath them. Again, a

seepage analysis must be made to determine the resisting load required of the

berm. Downstream slope stability of the embankment will normally increase

because of the resistance to sliding provided by the berm. Huntington District

has employed berms as remedial measures at several flood control dams in the

Muskingum River flood control system (Coffman and Franks 1982). Similarity of

the embankments and environments allowed a standard remedial action for several

of the dams at the downstream embankment toe. A 3- to 7-ft-thick pervious

blanket of appropriate length is placed over the soft seepage areas at the

downstream toe. This adds weight and provides a working platform for installation of relief wells at points of excessive seepage.. Another example of a

stability berm is given in the Addicks and Barker Dams example,

paragraph 12-7a.

12-7. Slurry Trench Cutoff. Two major technical considerations in the use of

slurry trenches as remedial seepage control measures are (a) the effect on

stability of the embankment due to excavation of the trench and the presence

of a vertical plane of relatively weak soil (in the case of a soil-bentonite

backfill) and (b) tying the slurry trench to other existing or proposed seepage control measures. If a competent upstream blanket exists, the trench may

be placed upstream of the embankment and tied to the blanket or may be placed

through the dam and any pervious substratum if stability requirements are met.

A cement-bentonite backfill may be placed in panels or a concrete wall may be

placed in separately excavated elements if an open trench and the relatively

weak soil-bentonite backfill are unacceptable because of stability risks. The

following experiences with slurry trenches provide general examples of this

cutoff type as a remedial measure.

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a. Addicks and Barker Dams, Houston, Tex. (U. S. Army Engineer District,

Galveston 1977a; U. S. Army Engineer District, Galveston 1977b; U. S. Army

Engineer District, Galveston 1983). Completed in the late 1940's, Addicks and

Barker Dams are rolled earth embankments providing flood control in the Houston, Texas, area, with respective maximum heights of 48.5 and 36.5 ft above

streambed. Neither normally impound water except in periods of rainfall. The

embankments contain some silts and sands, foundations have silt and sand

layers, and upstream borrow areas expose the foundation permeable layers. At

the time of construction, these conditions were not considered, significant

because of the large discharge capability and short detention time of the

reservoirs. Residential and commercial development of the downstream local

area caused several changes in operating conditions which increased detention

time and made the effect of seepage more critical. These included restriction

of discharge rates and construction of drainage channels on non-Federal land

within 200-300 ft downstream of the center line of the dams which expose the

pervious portion of the foundation. Erosion of the drainage channel slopes on

the side of the channel nearest the dam and boils in the channel bottom during

times of low reservoir impoundment indicated the potential for dangerous seepage conditions during high reservoir levels. Downstream piezometers also

indicated a quick response to changes in reservoir levels. This example

describes remedial actions at Addicks Dam; actions at Barker Dam were similar.

Several remedial measures were considered:

(1) Downstream drainage blanket and stability berm - rejected due to

requirement for additional right-of-way and Government responsibility for

maintenance of local interest's drainage ditch.

(2) Downstream drainage blanket, stability berm, and relief well system

and downstream slurry trench - (relief wells between embankment toe and slurry

trench) very positive control (blanket and berm control embankment seepage

while wells and slurry trench control underseepage), but very costly, longterm well maintenance required, and all seepage forces would be directed at

the embankment toe.

(3) Same plan as (2) except slurry trench replaced with steel sheet pile

cutoff - same reasoning as (2) except sheet pile would greatly increase cost.

(4) Slurry trench cutoff through embankment and foundation - a very

positive, controlled cutoff for embankment and foundation; no maintenance; all

work on Government property; less costly and quicker than other alternatives.

For most of the remedial work, alternative (4) was chosen, though for selected

lengths of the embankment where they were the best alternative, alternative (1) was used and some relief wells were placed. With a maximum depth of

64 ft and width of 3-5 ft, the slurry trench penetrated 2-4 ft into a relatively impervious clay underlying the pervious foundation materials. Figure 12-2 provides a general cross section of the design. The trench was

placed 10-20 ft upstream of the embankment center line with equipment working

from a platform established by degrading the upper portion of the embankment.

Cemented materials, present in some portions of the excavation, were broken by

dropping a 10-ton percussion tool on the cemented layers. Portions of the

trench collapsed but were successfully reexcavated. Additionally, small (3-in.

diameter) tunnels were encountered in the upstream side of the trench but were

12-7
12-8

PORTION OF EMBANKMENT THAT MAY BE REMOVED 

DURING CONSTRUCTION OF SLURRY TRENCH AND 

REPLACED AFTER COMPLETION OF SLURRY TRENCH 

UPSTREAM 

!i 

SLURRY 

TRENCH EXISTING EMBANKMENT 

DOWNSTREAM 

LIMIT OF DEGRADING 

3 - _;.r;:::-' 

R

...._ ....__2_, 1 EXISTING GROUND 

-

...._ /EL 99 4 _/EXISTING BERM CONSTRUCTE

EL 94.3--........ _..- _,.- _.-

-

- -- GROUND 

--

---f./to>---- 3' MINIMUM TO 5' MAXIMUM SLURRY 

TRENCH CUTOFF 

BOTTOM OF TRENCH CUTOFF VARIES 

TYPICAL SECTION 

STA 350+50 TO STA. 377+00 

NO SCALE 

Ci SLURRY TRENCH 

...._ ...t. 4 - L-- DITCH EXCAVA

1 L.:::..::..,_\: --:: ::::.._-=--= =-..

4.5 . 

ORIGINAL EMBANKMENT SLOPE 

TOP OF CLAY CAP 

" CLAY OR SANDY CLAY, (CH OR CL) LIMIT OF DEGRADING 

SLURRY TRENCH BACKFILL 

PROTECTIVE CLAY CAP DETAIL 

NO SCALE 

Figure 12-2. Addicks Dams remedial slurry trench for embankment and foundation s

83 control (from U.S. Army Engineer District, Galveston ) 
EM 1110-2-1901

30 Sep 86

plugged with cloth. Backfill gradation is shown in table 12-1. For some portions of the project, percent passing for the No. 200 sieve were 15-30 percent. Backfill mixing and transport to the trench were conducted in several

ways. Some backfill was batched dry, placed in concrete trucks with slurry

added, then mixed and transported to the trench. The higher fines content

backfill in some cases proved too sticky to mix in trucks. Mixing was conducted on the ground next to the trench but occasionally excess fines were

picked up from the working surface. A concrete mixing pad was used as an

alternative though wear from the mixing equipment destroyed the concrete.

Excess or unsatisfactory material was deposited in old borrow areas upstream of

the embankment to reduce underseepage. In one area, a slurry trench located at

the upstream toe of the embankment provided underseepage control while a downstream berm provided embankment stabilization. The berm of sandy clay had

permeability characteristics similar to the embankment and provided a 1V on 8H

slope. Several of the discharge conduits which suffered from seepage and piping were resealed, after cleaning, with ethafoam backer rods and a polyurethane

sealant. Where the sealant would not adhere to the concrete, joints were

talked with oakum soaked with a grouting compound. Well screens were placed in

weep holes to prevent loss of soil, and relief wells with submersible pumps

were installed. For certain portions of Barker Dam, use of an upstream clay

blanket and a downstream stability berm (1V on 8H) was more cost effective than

a slurry trench. There was intermittent surface exposure of pervious foundation materials and a source of CH materials for the blanket was available

within the reservoir. Prior to placement of the blanket, ponded water and soft

surface materials were removed. The blanket was placed in 8-in. layers and

compacted with tamping rollers at natural moisture content.

Table 12-1. Backfill Mix for Slurry Trench, Addicks Dam (a)

Sieve Size or Number

(U. S. Standard)

3 in.

1-1/2 in.

3/4 in.

No. 4

No. 10

No. 40

No. 200

Percent Passing

by Weight

100

95 to 100

80 to 100

55 to 100

40 to 80

18 to 45

10 to 25

(a) From U.S. Army Engineer District, Galveston. 85

Though not yet severely tested, the control measures have performed satisfactorily based on the following observations:

12-9
EM 1110-2-1901

30 Sep 86

(a) Foundation downstream piezometers do not respond to reservoir levels

experienced so far.

(b) Phreatic surface has been raised upstream of the slurry trench.

(c) No embankment seepage, but there have been no significant pools.

(d) Settlement plates indicate no significant settlement of the slurry

trench. Though the restored embankment has cracked in the area of the

trenches, inadequate compaction of the embankment fill is considered the

cause.

b. Wolf Creek Dam, Ky. (Fetzer 1979). Constructed in the 1940's, Wolf

Creek Dam is a 200-ft-high combination earthfill and concrete dam founded on

limestone containing shale and solution cavities. During excavation of a

10-ft-wide cutoff trench, several interconnected solution cavities were discovered in the limestone. These were backfilled for a short distance with

impervious material, and a 50-ft-deep single-line grout curtain was placed

beneath the bottom of the cutoff trench. In 1967, muddy flow was observed in

the tailrace, a small sinkhole developed near the downstream toe, and wet areas

existed near the downstream toe. In 1968, a larger sinkhole developed (13 ft

wide, 10 ft deep) and drilling revealed solution features running perpendicular

and parallel to the dam axis. It was concluded that reservoir water was

passing beneath the cutoff trench. Grout lines were placed along the dam axis

near the embankment-concrete contact and downstream of this area. During

1971-1972, an overall assessment of the seepage problem was made since the

remedial grouting had only addressed about 200 ft of the 4,000-ft embankment

portion of the dam. A diaphragm concrete cutoff wall was considered the best

solution because it could be installed without draining the reservoir, a very

costly operation due to reservoir use. Explorations , which included borings

spaced on 3.1-ft centers along the axis of the wall (parallel to the dam axis),

defined the depth and length of the wall. Depth was 10 ft below the lowest

indication of solution activity (maximum depth 278 ft) and length was 2,239 ft.

In 1974, a request for technical proposals resulted in seven proposals with two

acceptable. In the second stage, a bid invitation was issued and an award was

made for a wall in the area of the switchyard and 989 ft of the wall along the

dam axis. The award in 1975 was followed by a second competition and an award

in 1977 for the remaining 1,250 ft of the axis wall. The wall consists of

alternate cylindrical primary elements and connecting secondary elements

installed using bentonite slurry, figure 9-14. Primary elements are

2.17-ft-diam steel casings filled with tremied concrete (see table 9-8 for mix

proportions). Weak cement grout fills the volume between excavation walls and

the casing. A 25-ft-deep core hole was drilled beyond the bottom of each primary element to explore for cavities and was pressure-tested and grouted prior

to the placement of a closed-end primary casing. The primary element was

required to set for a minimum of 20 days before excavation of the secondary

element which is also filled with tremied concrete. Frequent piezometer

readings (as often as every 4 hours) were made during construction to determine

the hydraulic condition of the embankment and foundation and warn of any

potentially critical seepage conditions. Excavation and drilling were closely

monitored to observe any drill rod drops or mud losses. Sealers and reserve

mud, constantly on hand, provided for emergencies. Grout takes around

12-10
EM 1110-2-1901

30 Sep 86

the primary casings and volume of concrete used in the secondary elements were

closely monitored as was the embankment in general. Efficient management of a

large number of observations was necessary to determine the current condition

of the dam. The lack of major losses of slurry, grout, or concrete during

construction was probably due to the densely spaced borings and grouting done

during the earlier exploration program. Wall construction, completed in 1979,

took approximately 4 years and two construction contracts. Subsequent

piezometric levels indicate the wall is a successful seepage barrier.

c. Camanche Dike 2, California (Anton and Dayton 1972). One of several

earthfill dikes containing Camanche Reservoir, Dike 2, is a zoned earth embankment about 70 ft high founded on alluvium containing an upper 20-ft strata of

clayey sand underlain by layered silty-to-fine uniform sand stratum. The

underlying sand stratum varies in permeability with its lower portion containing gravel. Original construction involved extending the core horizontally to

the upstream toe and discing and compacting the top of the alluvium to 1,000 ft

upstream of the dike axis. This was expected to provide acceptable underseepage conditions , while providing the option of tying an upstream cutoff through

the alluvium to the core if operating underseepage conditions were intolerable.

After reservoir filling, underseepage proved extensive and flowed over downstream property. Lowering of the reservoir reduced the seepage and revealed

holes in the compacted alluvium upstream of the embankment. Several seepage

control methods, including upstream impervious blanket, grout curtain, relief

wells, downstream drains, sheet piles, and others, were considered. Evaluation

of the options resulted in choosing an upstream slurry trench. This method

provided a positive cutoff, minimized piping potential, allowed retention of a

partial reservoir, and was the least expensive of positive cutoff methods.

Placed 50 ft upstream of the upstream berm toe, the 1,660-ft-long slurry

trench, 8 ft wide, extended through the alluvial materials to a maximum depth

of 95 ft. Backfill specifications required a 4-in. slump and a gradation as

shown in Table 12-2. An 8- to 11-ft-deep sandy clay blanket protected by a

1-ft-thick cobble and gravel cover connected the slurry trench to the horizontal core extension. Excess slurry was blended into the top portion of the

blanket to decrease blanket permeability. Since slurry trench placement,

downstream piezometers reflect decreased influence of reservoir levels with

only very small seepage flows at high, prolonged reservoir levels. Two potential sources of seepage are the somewhat pervious bedrock formation which the

slurry trench is keyed into and the sandy clay blanket connection between the

slurry trench and extended core. Connection of the 8- to 11-ft-deep blanket to

the slurry trench after placement of the slurry was difficult and may allow

reservoir leakage into the alluvium. Placement of the blanket or a partial

thickness prior to slurry trench construction was recommended. This would

provide a platform for construction of the slurry trench and allow a more

secure attachment of the trench to the blanket. This procedure has been

standard practice on many subsequent slurry trench projects.

12-8. Relief Wells. Though Chapter 9 describes design and installation of

relief wells, additional factors must be considered when relief wells are used

for remedial seepage control. Relief wells can relieve excessive uplift and

potential piping when pervious layers are overlain by relatively impervious

strata by providing controlled release of relatively large volumes of water.

Relief wells, as compared with cutoffs, allow loss of reservoir water and

12-11
EM 1110-2-1901

30 Sep 86

Table 12-2. Backfill Mix for Slurry Trench, Camanche Dike 2 (a)

Sieve Size or Number

(U. S. Standard)

6 in.

3 in.

3/4 in.

No. 4

No. 30

No. 200

Percent Passing

by Weight

100

80 to 100

60 to 100

40 to 80

20 to 60

10 to 30

(a) Courtesy of American Society of Civil Engineers. 135

require proper handling of discharge flows and periodic maintenance. Flooding

and erosion from well discharges must be prevented. Wells may be installed

quickly with a minimum of downstream right-of-way and, in many cases, without

reducing reservoir levels. If high uplift is present, boring and installation

may be difficult requiring extra measures to keep the hole open and stable

until the screen and filter are installed.

12-9. Drainage of Downstream Slope. Seepage emerging on or at the toe of the

downstream slope will normally be controlled by one of the methods previously

mentioned, Expedient installation of filter materials and a toe drain can

help prevent piping of embankment and foundation materials and may increase

embankment stability, but will not normally reduce seepage quantities. If

seepage is confined to a small area or areas, horizontally drilled drains may

help control the problem (Royster 1977). Horizontal drains of slotted pipe

normally do not have a filter envelope and would generally be used for

"nuisance" seepage or as an expedient measure until a more permanent solution

could be installed.

12-12
EM 1110-2-1901

30 Sep 86

CHAPTER 13

MONITORING PERFORMANCE OF SEEPAGE CONTROL MEASURES

13-1. General Considerations.

a. Before seepage control measures are implemented, site characterization by thorough exploration and testing is needed to determine if the seepage

control measures will serve the intended purpose. Knowledge of the in situ

site conditions along with the purpose of the seepage control measure and its

physical dimensions will help determine' the overall number and the placement

of monitoring devices. Several factors which can be monitored that can lead

to a conclusion regarding the safety of a dam are: (1) progressive increase

in the volume of seepage flow, (2) removal of solids by the seepage,

(3) increased uplift pressures or locally depressed gradients, and (4) soft or

wet areas on the downstream embankment.

b. Monitoring the performance of seepage control measures can lead to a

collective conclusion drawn from several measurements. The most common and

easiest monitoring is to rely on visual observations along with careful surface inspections at predetermined intervals. Another type of monitoring which

should be completed before construction is the installation of piezometers,

observation wells, and drainage collection systems to determine a site dependent pattern of behavior. Finally, the actual structure should be monitored

by the installation of a site specific network of piezometers, observation

wells, and drainage collection systems with flow measurements designed for the

anticipated seepage problems. A regular review of the data collected will

generally detect major changes between subsequent readings but equally as

important are the long-range trends manifested by steady changes or intermittent surges.

c. If it is determined during the monitoring process that a possible

problem exists, an expanded instrumentation program may be needed. This could

include more piezometers, relief wells, etc., and a more extensive analysis of

the seepage water; i.e., both a physical and chemical analysis of the sediment

and water including temperature, salt content, and resistivity which could be

compared with samples from the embankment and possible seepage sources.

According to the complexity of the problem and/or the economics versus safety

involved a group of other studies could be added including, but not limited to:

resistivity and spontaneous potential of the embankment and foundation, dye

tracing, infrared (aerial or portable ground based), and seepage acoustic

emissions. In most cases, the scope of the monitoring program will be determined by the economics involved.

13-2. Piezometers for Seepage Pressures.

a. Foundation. To determine the performance of seepage control measures,

a pattern of behavior should be established prior to and during construction

where long-term trends can be related to design or seepage conditions. Piezometers should generally be installed in all compressible foundation soils, the

number being dependent on the extent and thickness of the strata. If possible,

foundation piezometers should be installed-in the sections selected for embankment piezometers and should extend beyond the upstream and downstream toes a

13-1
EM 1110-2-1901

30 Sep 86

distance equal to the expected migration of pore pressures. An effective

piezometer installation plan should convert preconstruction piezometers into

postconstruction seepage monitoring piezometers for an effective continuity of

data. Shown in figure 13-1 is an example of a piezometer installation with the

embankment resting on a compressibility foundation (Chapter 9) and an impervious core cutoff through a sand and gravel layer. Effectiveness of the cutoff

and the presence of uplift pressures can be evaluated. Shown in figure 13-2 is

an embankment with an impervious core that intercepts a pervious soil and rests

on the top of rock (Chapter 11) and again the effectiveness of the cutoff

and/or the integrity of the rock can be evaluated. Shown in figure 13-3 is an

embankment founded on a thin impervious top stratum underlain by a deep zone of

pervious material (Chapter 9). In this case a cutoff was impractical and seepage pressures are simply monitored beneath the dam to determine time effects on

the control measures while the effectiveness of relief wells downstream is

determined with foundation piezometers. An effective monitoring system should

also include piezometers in the abutments to determine the effectiveness of

drains and/or of the embankment-abutment interface which could include grout

curtain cutoffs (Chapters 10 and 11). Also artesian flows may exist in the

abutments and need to be monitored. Shown in figure 13-4 is a piezometer

installation that is used to monitor a grout curtain cutoff and cut-slope

drains. Remedial seepage control measures, discussed in Chapter 12, might

require additional piezometers to monitor both the installation and the effect

of the new measures.

b. Embankment. As discussed in Chapter 8 three methods for seepage

control in embankments are: (1) flat slopes with or without drains,

(2) embankment zonation, and (3) vertical (or inclined) and horizontal drains.

An embankment with flat slopes (as defined in Chapter 8) constructed of impervious material, and which has infrequent high reservoir levels, should have

only enough piezometers in the embankment to establish the phreatic surface.

A typical example is shown in figure 13-5. To monitor seepage control

measures in a zoned embankment (Chapter 8) the number and spacing of piezometers depend not only on the height of the dam but also on the material properties of the zones. The core must be monitored to determine the phreatic

Figure 13-1. Example of foundation piezometer installation of Surry Mountain

Dam (from EM 1110-2-1908)

13-2
13-3

LEGEND 

o EMBANKMENT PIEZOMETER 

• FOUNDATION PIEZOMETER 

PERVIOUS FOUNDATION 

SOIL·S 

40 

i 

SCALE IN FEET 

0 80 

N

Figure 13-2. Piezometer installation for dams on pervious foundations

EM 1110-2-1908) 
13-4

0 U.AI!IANK'-IENT PIEZOMETER 

e FOUNDATION PIEZOMETER 

RCLArtVELY PERVIOUS 

UNCOMPACrCD MArERIAL 

RCLAriVELI' 

PERVIOUS MArERIAL 

f.-AXIS Otr DAM 

I 

e SAND AND GRAVELS 

TERTIARY CLAYS AND GRAVELS 

SCALE IN fEET 

40 00 

NOTE: ALL PIEZOMETERS ARt O

TYPE. PROJECT CONTAINS 

OF INSTRU'-IENTATION TH

SHOWN. 

• 

Figure 13-3. Piezometer installation with a thin impervious topstratum and reli

systems, Enid Dam (from EM 1110-2-1908) 
13-5

; 

8 & 

A-111 

A·ZIID 

LEGEND 

D STRONG MOTION ACCELEROGR&PH 

SHELTER 

5 SURFACE MONUMENT 

liD A TYPE PIEZOMETER (FOUNDATION) 

TRIGGER AND POWER CABLE ALIGNMENT 

FOR STRONG MOT ION AGGELEROGRAPHS 

(SEE SHEET 253) 

' 

I 

I 

I 

• 8 

SA· S 

! SEE SHEETS 249 AND 251 

FOil LOCATION) 

0 

8 

PLAN & 

SURFACE MONUMENT , PIEZOMETER AND 

STRONG MOTION ACCELEROGRAPH SHELTER 

100 1) 100 zoo 

Figure 13-4. Piezometer installation for dam abutments having grout 

curtains or cut-slope drains, Applegate Lake Dam (from U. S. Army 

Engineer District, Portland104) 
13-6

o?o 

S60 

650 

J €>40 

"' 630 

ti- b20 

w 

.... 

;;e 610 

GOO 

j: 590 

'580 

w 

570 

se.o 

550 

D\STANCl IN f'EET I="ROM or OMvl 

800 700 600 500 400 300 200 \00 0 \00 200 300 

,-.-----T - --- T --- T T- r---·r-------r-- y-----T -

SELECT IMPERVIOUS 

FILL----

18 "RIPPAP ON 6 "8£0/)/A/r. -

24 (}N 4 ,.8!00/NG 

FLOODPLAIN C:MBANKM£NT SECTION 

STATI0"-1 IOCHC>") TO STATION 

sor; 6C:i 

-r --r- 

3' HO/'!Z0/1/r/

ORfil•'-46£ R! .• 

[OUFrTOf' S

Figure 13-5. Estimated seepage for Aubrey Dam, Texas (from U. S. Army Engin

District, Fort Worth81 ) 
EM 1110-2-1901

30 Sep 86

surface and in situ permeability. Using this information, cracking potential

can be estimated. On either side of the core there can be filters, transition

zones, random zones, outer shells, and blankets (Chapter 8). In general, the

different zones should increase in permeability outward and should have

piezometers in each zone. During rapid reservoir drawdown, the upstream

piezometers would detect excess pore pressure buildup while during conservation and high pools, all the piezometers would indicate the effectiveness of

the zones and check design values. A typical installation in a zoned embankment is shown in figure 13-3. In a zoned embankment the piezometers located

near the upstream core face can be instrumental in determining the development

of cracking in the core (Vaughan et al. 1970). Depression of the piezometric

elevation in a localized area (cone of depression) can indicate velocity head

loss which would indicate leakage through the core. Remedial work for

Baldershead Dam (Vaughn et al 1970 and Lovenburg 1974) included placement of a

large number of piezometers near the upstream face of the core (figure 13-6)

which were successful in indicating piezometric depressions.

c. Drains. The purpose of vertical (or inclined) and horizontal drains

is to control seepage either through the embankment or beneath the dam (underseepage). A vertical (inclined or horizontal) drain in the embankment may be

used as a filter to prevent material from eroding from the core and/or as a

method of collecting seepage exiting from horizontally stratified soil layers.

Enough piezometers should be installed in the drain to determine if the seepage is coming through the embankment material or if it is underseepage, figure 13-7. If the horizontal drains intercept underseepage which in turn is

drained by lateral drains, piezometers should be placed on either side of the

laterals to determine their effectiveness, figure 13-8. Long-term trends

(pressure buildup or depression) detected in the drains not directly related to

the reservoir level could indicate either clogged drains (pressure buildup) due

to embankment or foundation material moving into the drains or piping and

erosion (pressure depression) due to material moving into pipe drains, high

permeability zones, or into fractured rock. Toe drains are effective in collecting seepage and preventing saturated areas along the downstream toe.

Piezometers in or near toe drains would only be effective when a downstream

blanket has been added and uplift pressures need to be measured. Drainage

galleries and tunnels are used mostly in abutments in the United States to

intercept and control seepage in fractured rock. Drainage tunnels along

extensions of the dam's axis or in downstream abutment areas serve to collect

seepage. Piezometers located near the drainage tunnels would indicate the

effectiveness of the tunnel. Cut-slope drains can be used to intercept seepage and collect drainage along abutment slopes while piezometers placed both

upstream and downstream of the drains can determine effectiveness of the collection system, figure 13-9.

d. Downstream Areas. Seepage can migrate beyond the embankment toe

particularly in clay shale or fissured formations. Geologic site characterization in most cases will determine the need for piezometers downstream of the

toe but if there is any doubt they should be installed in the questionable

formations 50 to 150 ft beyond the toe, figure 13-1. Piezometers should also

be installed downstream of the outlet works, spillway, and stilling basin if

they extend well beyond the toe and are not close to other piezometers.

13-7
13-8

GROUT TREATMENT 

BOO 

DIAPHRAGM WALL I I 

Ol 0 100 200 300 400 500 609 

330 

320 

310 

300 

290 

280 mO.D. 

340-330-

& 320-

290-

280-

ICEY 

t Multi-unit pie20111eter 

I 

1 standpipe 

<:,asogrgnde-type poeZCMMter 

SECTION AT CH. 372 

610 620 630 640 

335 

330 

325 

320 

315 

310 

Nowat.rWATER TESTS I I I I I 

water loss 

ADDITIONAL PIEZOMETERS 

650 660 

I I I I 

INSTALLED IN 

670 

Figure 13-6. Layout of Baldershead Dam piezometer installation in upstream sha

(courtesy of British Geotechnical Society212 ) 
13-9

LEGEND 

• SUFFACE MONUMENT 

+ POPE PRESSURE DEVICE IN SILT FOUNDATION 

..t. EMBANKMENT PORE PRESSURE DEVICE 

(!} PIEZOMETER IN FOUNDATION ROCK ABUTMENT 

IS PIEZOMETER IN NATURAL GRAVEL AQUIFER 

• PIEZOMETER IN BLANKET DRAIN 

Q PIEZOMETER IN FOUNDATION TILL (AT T.R.) 

TYPICAL SECTION- FLOOD PLAIN 

SCALE OF FEET 

bea:. Y •lo 100 I 

Figure 13-7. Piezometer installation for dams with through seepage and u

79 U. S. Army Engineer District, Baltimore ) 
13-10

20' MAINTENANCE BERN 

rRANSITION MATERIAL j_ ROCK""' 

l 

OOWNSTREAM 

HP 04lPAOJI 

TYPICAL SECTION- VICINITY STA. 56+ 50 

LEGEND 

• SURFACE MONUMENT 

+ PORE PRESSUPE DEVICE IN SILT FOUNDATION 

.t. EM :JA "KM[NT PORE PRESSURE DE VIC[ 

0 PI[ZOME TER IN FOUNDATION ROCK ABUTMENT 

S PIEZOMETER IN NATURAL GRAVEL AQUIFER 

• P1EZOMET£R IN BLANKEr DRAIN 

<> P1EZOM£TER IN I OlltWAIION TILL (AT T.RJ 

00 

SCALE OF FEET 

.., IDO 

SUSQUlttAirfNA ftiY

TIOGA· KAWIIIOND 

INSTRUMENT

HAMMOND 

TYPICAL SEC

Figure 

u. 

13-8. Piezometer installation for dams with lateral drains (from 

S. Army Engineer District, Baltimore79 ) 
13-11 / 

•-••cr-t:•n 

A TT"' I'IU:OifUIIIII'OUifDoUICNII 

- TIUIU:II •110 IIOWIII c•kl •t.IIIIIIIIIT PLAN J:h 

SUftfAt:l[ MONUMUT , "UOM[T[ft AND 

SECTION@ 

DOuel.[ WEill fOft 

f'tf'ELINI[S 'A' AM) 'W 

DRAINAGE SYSTEM PLAN 

Figure 13-9. Drain and piezometer installation, Applegate Lake, Oregon (fr

U S A E · D · · Portland104 • • rmy ng1neer 1str1ct, ) 
EM 1110-2-1901

30 Sep 86

e. Near Relief Wells. If a relief well system has been installed, pore

pressures should be checked in the vicinity to evaluate the efficiency of the

system. Piezometers should be located both upstream and downstream of the

relief wells and should intercept the stratum being drained, figure 13-3. If

there is a line of wells, piezometers should also be installed generally at

the midpoint between the wells or at the point expected to have the highest

pore pressures.

f. Spillways, Stilling Basins, and Outlet Works. Underseepage control

beneath the stilling basins of spillways and outlet structures founded on pervious foundations is generally provided by drainage blankets supplemented in

the case of stratified foundations by deep well systems (figures 13-10 and

13-11). Drainage blankets extend beneath the chute slabs, if necessary. As

shown in figure 13-10, piexometers should be installed to check the effectiveness of the drainage blanket and relief wells, and to check pore pressure

beneath the outlet channel and against the stilling basin walls. Piezometers

are used to check pore pressures occurring below the relief well system (figure 13-10). Generally, a sheet pile wall, with a minimum penetration of

15 ft, is installed along the downstream toe of the stilling basin to control

piping and a piezometer installed downstream of the wall is needed to determine the effectiveness of the wall.

13-3. Flow Measurements.

a. Weirs. Seepage flow measurement is an important parameter of dam

performance. Most installations have used a relatively simple weir, measuring

the seepage over brass or stainless steel 90-deg V-notches like the collection

system shown in figures 13-12 and 13-13. A number of weirs can be installed

in drainage galleries to determine flows from different sources, i.e., left or

right abutment, dam underseepage, and total seepage. A certain amount of

sediments will settle out just upstream of the weir which is important if the

sediment load is not continuous and occurs between visual inspections. If the

seepage is exiting downstream of the dam and outside of a drainage collection

system, a weir pond can be formed in conjunction with the V-notch weir for the

specific purpose of determining long-term sediment content in the seepage.

b. Flumes. A flume is a short rigid-walled channel designed to constrict the flow and so give rise to critical velocity. A single measurement

of water level is sufficient to measure discharge at critical velocity. The

most commonly used flume for seepage measurements is the Parshall flume as

shown in figure 13-14. Empirical charts for flow discharge have been developed for specified flume dimensions (Bureau of Reclamation 1967). The flume

can be fabricated and placed in seepage flow that has been channelized. This

method is a relatively rapid and simple way to obtain precise flow

measurements.

c. Relief Wells. Relief wells, as the name implies, are widely used to

relieve pressures and control seepage through pervious strata beneath earth

dams, spillways, and outlet works. A thorough knowledge of the geologic conditions and characteristics of the soils at the dam must be available to

design a system as part of initial construction or as remedial work. To be

effective, the well must flow but must not allow the loss of foundation

13-12
13-13

;.;::_. ----

... ...... , 

C[Ntr• II" reorn ( 

llt•nuttol .. 1-1 •f p.rr-.-.# ..,.,...,,J __ _,., .. 

....... 

e ,.._., Nl:n•• "lo.cr .. ._.._.. 

• "..,.._,""•"""'•n••'"u..t 

• Af.ZOIIU."'tTR 

OUTLl

PLAN 

w IIMI.I.Y 

I "' 

Cll'fiC.I. 01 TMI. .........

w•aa 

Figure 13-10. Piezometer installation for dams with outlet structures (adapted 

U. S. Army Engineer District, Vicksburg 115) 
13-14

S"'ILL

COMPLET

>fO I :IOOC:C.t K .... '( t•I

..... I I < 1 • •t 

C"+Cf M Tfll l"tllil&ID(NT, '

..... S · 

Su-ftlO 

Figure 13-11. Piezometer installation for spillways (adapted from U. S. Army En

District, Vicksburg 115 ) 
EM 1110-2-1901

30 Sep 86

Figure 13-12. Installation of drainage system with weirs (from

U. S. Army Engineer District, Portland 104

)

13-15

SLOPE VARIES 

MAX 5 • 0.0100_ 

OliN. 5 • 0.0020 

PIPELINE A A 

REGULATING OUTLET 

CHANNEL 

EL. 1762.:1 

ADJUST SLOPE TO CONFORII \ WITH TOP OF ROCK 

MIN SLOPE • 0 0020 

,----~~=-=T~-=---~ I TYPE m1 ~--~==~~--~ ~~==~~~~~~_oEL.1772.~ r---••o'---1 - •I ~~ .... ... ----_-:;_-_-_-_-__ 

RIQ Ct<AHNEL 

PIPELINE C 1773.~ 

PROFILES ALONG ft. OF DRAINAGE SYSTEM 

NOT TO SCALE 

_)__,.,..._____. ------- -~--- - ~~~ .... _R2_~EYoSED _l:~oDOS ANO Sci)P£.!_ 

7111A1t01 ~---: R£VrS[D -~----PLAN A~ PA()fll.£S ;.~~--- ~ 'J. S, --y £NQ!t-IE~ OISTRICT, PORTI.ANO 

- ROGUE ~IVEA BASIN OREGON 

-x;,s APPLEGATE RIVER 

APPLEGATE LAKE 

~ 

- EMBANKMENT DAM EMBANKMENT 

DRAINAGE SYSTEM -.fwt!. PLAN AND PROFILE 

::::t~~~..H'-.- -------- ~~, Dol'~"-: Tl hA-..OL 

4~tl~••&.\\···ot(l0 

~~If-. . -•n >o AGE -1-1/23 
13-16

_ \ CMP 

PLAN - DOUBLE WEIR 

} -SELECT 

BACK FILL 

MINIMUM EXCAVATION LINE 

SECTION @ 

SCALf 112•• 1'0' 

SELECT BACKFILL 

WEI A BOARD 13 REQUIRED) 

SCA&..l. ,. • ··-o• 

,. __ ,,, __ 

• .,_..UA 

., •tt:lt ..... -

I 1/.l•.x 1/4••,.••• st- Hit• • _,, 

,..,. 

(1/JIIS'flll .. , U.l •t lttltlltll,..,,..,._,."'''., 

.,.. . ., "•"'-'••' 

SECTION E-E 

JIQ SCAll 

FURNISH AND INSTALL I" MARINE PLY 

SECTION @ 

SCAlE 1/ 2" • 1' 0" 

U. S. ARMY ENGINEER DISTR

--

ROGUE RIVER B

APPL£G4.

APPLEGA

EMBANKMENT DAM 

DRAINAGE 

DETAI

Figure 13-13. Typical weir installation (from U. S. Army Engineer District, 

Por
EM 1110-2-1901

30 Sep 86

Figure 13-14. Modified Parshall flumes of 6- to 65-second-foot

capacity (after Bureau of Reclamation24 )

material which could lead to piping or erosion failure. A frequent use of

relief wells is near the downstream toe of a dam to control seepage through a

pervious zone, figure 13-13. A toe drain is used to collect the flow while

weirs in the drains or manometers on the wells can determine the quantity of

flow. Relief wells can be pumped to determine the effect on surrounding

ground water and the permeability of the soil near the well. In many cases

where dams are built on jointed or fractured rock, grout curtains are used as

seepage cutoffs. It has been found in some cases that grout curtains do not

appreciably affect the uplift pressures downstream of the curtain and that a

series of drainage wells is a more effective tool to reduce uplift pressures

when the volume of seepage loss is not a problem and when the high cost of

grouting is hard to justify (Casagrande 1961). Relief wells have been successfully used when the pervious strata is too deep and wide-ranging to

effectively use any type of positive cutoff. Relief (drainage) wells are used

beneath spillway and outlet works slabs to relieve excess pressure in the

rock, the underslab drains, or a pervious strata. An example of a group of

wells designed to relieve pressure under an outlet works stilling basin is

shown in figure 13-10. Relief wells can be used in rock abutments to intercept seepage and to control artesian flow.

d. Seepage Outlets. Monitoring seepage outlets downstream of the dam

is handled according to the present severity of the problem or to future

associative problems if the seepage worsens. A small wet zone near the toe

might require only routine visual examination as would a small trickle from a

rock abutment. If there is sufficient seepage to measure, an effort should be

made to estimate the volume with a container and a stopwatch and to note sediment content. Operation and maintenance personnel should be trained to

13-17
EM 1110-2-1901

30 Sep 86

observe the situation especially during high reservoir levels. All seepage

outlets should be monitored to determine long-term trends. Sand boils developing downstream require immediate attention. An estimate of the pore pressure involved can be determined by sandbagging around the boil to measure the

height of water rise. If the seepage exiting at the toe or abutment is severe

and will require remedial work but the dam is not in imminent danger of failing, collection systems must be designed as a pattern develops. Temporary

control measures such as toe drains and surcharge berms might be installed

with weirs to establish the severity and the trends of the seepage for use in

design of remedial work. Any changes noted during monitoring, i.e., volume

change, sediment load change, etc., should be considered important. After the

remedial work has been designed it may include any number of the monitoring

systems discussed previously in this chapter. If the seepage is exiting from a

drain system that is not being monitored internally, visual monitoring should

continue at specified intervals and during heavy runoffs and high reservoir

levels.

13-4. Seepage Water Analysis.

a. Physical Analysis. Physical analysis of the seepage could include

information on suspended solids, temperature contours, and water resistivity

values. This information may be obtained from physical testing of samples or

by remote testing techniques.

(1) The amount of suspended solids in the seepage is an indication of

material movement and piping. Although there are obvious problems with muddy

or turbid flow, seepage which appears clear may often carry small amounts of

suspended solids that would be detected by occasional samples and analysis.

Sediment traps built in conjunction with manholes and weirs can be used to

indicate the amount of suspended sediment and to obtain samples for chemical

analysis.

(2) Several different methods of measuring temperature are designed to

help locate seepage areas not yet visible and to trace seepage from its origin

to its exit. One remote sensing method (U.S. Army Engineer District, Los

Angeles 1981) is an aerial survey which includes any or all of the following:

(a) color photography, (b) color infrared photography, (c) thermal infrared,

and (d) color oblique imagery. The basis for the study is that different

materials (wet or saturated versus dry) possess different heat absorption

rates; therefore, heat radiation rates will differ. Since the specific heat

of water is higher than soil or rock, a warm zone in a known seepage area is a

suspected seepage outlet. This method is intended for large areas but smaller

areas can be covered by thermal infrared using portable hand-held units (Leach

1982). A second method of thermal monitoring (U. S. Army District, LOS

Angeles 1981) is to physically place an array of gages in and adjacent to the

embankment and measure the diurnal temperature (temperature below the reach of

the surface but within the annual temperature zone). A temperature fluctuation is interpreted as seepage related and becomes the basis for further study

in that zone. A vertical thermal contour can be made in present open system

piezometers or in remedial planned piezometers, again with temperature fluctuations or inversions interpreted as seepage related (U. S. Army Engineer District, Los Angeles 1981 and Leach 1982). These data are interpreted or

13-18
EM 1110-2-1901

30 Sep 86

expanded by determining the temperature stratification of the reservoir, the

temperature of all known seepage sources, and the temperature at the seepage

exits.

(3) Seepage can be monitored by the physical detection of tracer elements such as dye and isotopes that have been introduced upstream of the seepage exit either in the reservoir or a piezometer close to the suspected seepage path. The dye selected should have a favorable absorption and decay rate

and should meet state water quality control requirements. Samples taken from

piezometers, drains, and downstream exit points are monitored using an instrument capable of measuring parts per billion, e.g., a fluorometer for fluorescein dye. By recording time of arrival and concentrations, interpretations

can be made as to the source of the seepage and the permeability of the strata

along the path of seepage. Environmental isotopes are also traced by obtaining samples which can be measured by a mass spectrometer for oxygen -18 and

deuterium and by the low level counting system for tritium.

(4) Another physical property of the seepage that can be measured is

its conductance or resistance. Resistance which would be defined in the field

by a resistivity survey is a measure of the ability to resist current flow

through the seepage, a factor that is altered by the introduction of salt compounds, graphite, etc. A thorough sampling program from all possible sources

of seepage, all seepage exits, and all available piezometers can produce a

group of resistivity values that is an important tool in defining seepage

sources and possible paths. Using the geologic profile for the site, and by

comparing individual resistivity values or by comparison against a range of

known values (Telford et al. 1976), an interpretation as to the source of the

seepage and the strata through which it travels can be made.

b. Chemical Analysis. To monitor and interpret the chemical composition of seepage requires a thorough knowledge of the surrounding geology or

chemical analysis of samples in the different strata. If possible, a preconstruction chemical analysis should be conducted on all water sources and on

any formation that might contribute minerals or salts or that might affect

acidity or alkalinity.

(1) One important chemical property would be the salt concentrations in

the seepage. In this case to determine correlations, reservoir and groundwater concentrations are essential along with the mineral content of the area,

e.g., water flowing through limestone would generally increase in chloride

concentration. Minerals such as feldpoid sodalite and apatite (Turkish

National Committee 1976) or caliche in volcanic regions (U. S. Army Engineer

District, Los Angeles 1981) can release chloride ions into the water. Interpretation of chloride concentrations and its long-term trends can help determine the relative length of seepage paths (shallow or deep seated), the extent

of the leaching of the formation (whether concentrations are constant,

increasing, or decreasing), and the source of the seepage (comparable concentrations). Interpretation is sight-dependent and any of the above or possibly

other conclusions may be reached.

(2) Another chemical property needed for interpretation is the mineral

content of the seepage. Mineral concentrations of calcium and magnesium

13-19
EM 1110-2-1901

30 Sep 86

bicarbonate containing dissolved carbon monoxide increase with length of flow

through a limestone formation while flow through some clay minerals may

increase concentrations of calcium and magnesium. Again, interpretation is

site dependent and requires a thorough knowledge of the existing conditions.

(3) Stiff diagrams, as shown in figure 13-15, are a graphical method of

presenting the anions and cations that are dissolved in the water (Hem 1970).

The Stiff method uses ions plotted in the same sequence to give an irregular

polygonal shape or pattern. In tracing the movement of seepage water, the

Stiff patterns are plotted on a map of the site for various locations downstream of the dam and the reservoir. The Stiff patterns may yield information

regarding the path(s) of seepage from the reservoir, prior land uses downstream of the dam (feedlot, septic field, etc.), and type of formation

(gypsum, dolomite, etc.).

13-5. Remote Sensing Methods.

a. Resistivity and Spontaneous Potential. As part of a total seepage

study, resistivity and spontaneous potential methods have been used successfully for seepage delineation in soil and rock (Cooper and Bieganousky 1978;

Cooper, Koester, and Tranklin 1982; and Koester et al. 1984). Resistivity

surveys used as part of a seepage study help identify possible zones of high

moisture as a function of depth and location. After the surveys are correlated

to previous borings or geologic information, new borings are placed in the

seepage flows. Spontaneous potential surveys are used to detect negative D. C.

voltage anomalies in the surface electrical field which have been found to

indicate zones of seepage flow (Cooper, Koester, and Tranklin 1982; and

Koester et al. 1984). Although flow is indicated, depth to flow can not be

determined for a given anomaly.

b. Photography. Methods using color, color infrared, aerial and ground

base thermal infrared, and color oblique photography were discussed previously

in paragraph 13-4.a.

c. Refraction Seismic Surveys. Seismic surveys can be used indirectly

in a seepage study by providing a bedrock profile that can be used as an aid

in determining the location and depths of observation wells, piezometers, and

relief wells. It is a quick and inexpensive method for obtaining subsurface

profiles.

d. Seepage Acoustic Vibrations. Acoustic emissions are the noises

generated whenever a material deforms or possibly by seepage whenever there is

turbulent flow against and around a casing (Koerner, Lord, and McCabe 1977).

The technique has been used to detect seepage by placing an accelerometer on a

waveguide that extends to the bottom of a borehole and recording the vibrations

present (Koerner, Lord, and McCabe 1977; and Leach 1982). Increases in emissions activity are interpreted as seepage flow. A similar technique that

consists of lowering an acoustic microphone down into a reservoir has been

used to detect leakage on the upstream asphalt-covered face and in the reservoir itself (Coxon and Crook 1976). One disadvantage would be high background

noise levels.

13-20
EM 1110-2-1901

30 Sep 86

Figure 13-15. Stiff diagram used to graphically present

anions and cations in seepage water (from Hem 1970)

13-21

30 

--rNe+K~----t-----~~~~~~+-----+---~a 

·C.~----t-----+-----+-----+-----+---~HCOa 

Ma~--~~--~-----+-----+----~----~so. 

F•~----t-----+-----+-----+-----+---~co, 

u 20 15 10 5 

CATIONS. IN MILUEQUIVAU:NTS 

PER UTER 

0 

12-6 

15-l 

10 

ANIONS, IN MILLIEQUIVALENT$ 

PER LITER 

25 
EM 1110-2-1901

30 Sep 86

CHAPTER 14

INSPECTION, MAINTENANCE, AND REHABILITATION OF

SEEPAGE CONTROL MEASURES

14-1. Introduction. Proper functioning of seepage control features requires

adequate maintenance, inspection, and, if necessary, rehabilitation. Some

seepage control methods such as relief wells are in the best condition they

will ever be the day they are installed and developed, while others such as

soil-bentonite slurry trench cutoffs may increase in effectiveness with time.

All seepage control features must function effectively for the life of the dam

or be rehabilitated or, if necessary, replaced. The effectiveness of some

seepage control methods, such as the toe trench drain, may be directly

observed. For other seepage control methods, such as cutoffs, performance

monitoring (see Chapter 13) is essentially the only means of determining the

degree of effectiveness.

14-2. Inspection. The procedure for periodic inspection and continuing evaluation of dams is given in ER 1110-2-100. Procedures for reporting evidence of

distress in dams are given in ER 1110-2-101. Procedures in these two ER's are

often supplemented by Division Regulations as well. Details concerning the

monitoring performance of seepage control measures are given in Chapter 13.

The first general field inspection for new earth and rock-fill dams is carried

out immediately after topping out the embankment. The initial inspection of

concrete dams is accomplished prior to impoundment of reservoir water. The

second inspection for earth and rock-fill and concrete dams is made at a

reasonable stage of normal operating pool but no later than one year after

initial impoundment has begun. Subsequent inspections will be made at one-year

intervals for the next four years, at two-year intervals for the following

four years, and then may be extended to every five years if warranted. The

periodic inspections provide the opportunity for a group of specialists to

critically examine a project for existing and/or potential problems, to recommend remedial action or changes in instrumentation , and to direct the attention

of the operating personnel toward the significant and critical features of a

project. However, the occasional inspection cannot take the place of daily

observations required to detect potentially dangerous problems at an early and

repairable stage. Table 14-1 outlines the inspection, instrumentation, maintenance, and rehabilitation of seepage control facilities. Some seepage control

methods such as embankment zonation, cutoffs, and upstream impervious blankets

are not amenable to visual inspection. Other methods such as flat slopes

downstream of the dam and downstream seepage berms are most accessible and

should be inspected daily during periods of full reservoir pool to ascertain

that they are functioning properly in controlling seepage. Other seepage control facilities should be inspected on a regular schedule as shown in

table 14-1.

14-3. Maintenance. Timely performance of maintenance on seepage control

facilities is required for the facilities to perform satisfactorily. Some

seepage control methods such as flat slopes downstream of the dam and downstream seepage berms are accessible and require maintenance. Other seepage

control methods such as embankment zonation, cutoffs, and upstream impervious

blankets do not require maintenance. However, maintenance is required on the

instrumentation used to evaluate the degree of effectiveness of all seepage

14-1
EM 1110-2-1901

30 Sep 86

14-2

Seep••• Control P•c.UitY 

Plat elope• Vithout 

drain• 

Vertical and horizontal' 

~~train• 

Hortaontal drain 

Cutoff 

c .. poeud baekt111 

treneh 

Slurry trench 

SoU-be-ntonite 

Ce•ent-bentonite 

Concrete w•ll 

Upetr••• iaparvioua 

blanket 

Downuna• aeepage bera 

Toe trench dr.ain 

bltef velle 

Con.crete galletietl 

Upstreu iapervtoua 

blanket 

Relief wlla 

Control of S••e••• 'lbroup Eabankaent 

Dally 

Weekly 

Wukly 

Dolly 

w .. kly 

Wet •pot•. •louch ... tna, •roaton 

Turbidity and diacharge rate 

Turbidity and diochat·a• rate 

See pas•, boil•, 

erosion 

Tnbldity ond dhc:hAr&• rau 

Vat hi (b) Flow nte and sand 

Wtokly 

infUtrat1on 

Turbidity and dhch•rs• rau 

Monthly Surf•c:e IIODUMI'I.U 

Yari .. (b) PIIIOM:ter 

Variu(b) PUia.eter 

Control of Under•••p••• 

V.eriel(b) PiiiOMter 

Varie1 (b) 

Vorho (b) 

Yarho(c) 

Monthly 

Ptezoaeter 

PieiOHUt.' 

R•••rvoir 

eediMntation 

Ph.aoeeter 

Control of. Seep••• Throuah Abut•ent 

Weekly Turbidity end d11-

c:harl• ratl 

Varh1 (b) Plow rate and sand 

tnfiltrat1on 

Var:lee (b) Reeervoir 

eedillentation 

!JM of Haint•aance 

Pertilid.nl, .ow- ina, flll1na 

(d) 

(d) 

(d) 

__ (d) 

(d) 

(d) 

(d) 

Fertilizin& • .avtna, fUHna 

Chock partodically<•l 

Method of R•h•bilitation 

btond dop41 thtckDan 

and lonath 

lnatall •hart parallel 

adjlcent tr•nch 

lnetall ehot:t parallel 

adj1c1nt tr1nch 

Fillina by bars• duapinl 

or follovins r•••rvoir 

drevdovn 

Extend bn·• thlc:ka.ell 

and lenath 

Chock par1od1cally(f) RohabUitate ... u. 

Check parlodicolly <al 

Filling by barge duapina 

or followina reetrvoir 

dravdovn 

Chock periodtcolly(f) Rehob!l1tate vella 

Control of Stepaae Beneath Spillways and StUUna 8a11n1 

Dra1naa• blanket Weekly Tqrbidity and dh- Variea (b) Piezouter 

chars• rate 

Var'he (b) Flow rate and 1.and Varies (b) Piezo.e ur 

lnt'iltraticm 

(d) 

Chack. ptriodically(f) Rehabilitate vella en 

unwatertna of 

structuTe 

(a) Schedule to be folloved upon obtainaant of full reservoir pool. The schedule durina initial fillin& will ba deterained durin& th.e initial 

periodic inapection. 

(b) Obearvat tou should be aad~ one week after ...xiatl• reservoir level and at three aubsequent fall ina raa&rvoir ataaea. 

(c)V.eries dttpencUn& upon potential aed:t .. ntation probleM, 1..,act on project perfo~nc:e,. and: t..pact on 1tre .. ayat .. (aae EM 11 t0-2-4000). 

(d}Rialna or f'aUtn& bead test abould be conducted on pier.oaeteu annually before the atora.,e aeaaon (Me EK lil0-2-1908, Part l). 

(e)C.tcb baelu, unholea, ditcbel, drainage pipe, and weir• ahculd be cle&ned, •• • ainiau. in thtl! fall tn preparation for the vlnter 

••••on, and •aa1n in the apring. 

(f} Annually. before atoraae aeaaon, c:h&ck valva a, aaak.ata, vall au.rda. cover pl1tea,. flap aataa em the outl•t• and other appurtanaa:c&s (see 

EM liiQ-1-1908, Part 1). 

(&)Should be axaatned fo-r atra•• cract.. hula••· •hUta of ali&ftiMnt. ••ce•atve lealc.a&•• &net dabrt• cleaned fr,._ &utter• and weirs. 
EM 1110-2-1901

30 Sep 86

control methods. The type of maintenance to be conducted on seepage control

facilities is given in table 14-1.

14-4. Rehabilitation. Inspection and maintenance of seepage control facilities may indicate the need for rehabilitation. The type of rehabilitation to

be conducted on various seepage control facilities is shown in table 14-1. If

the seepage control facility cannot be satisfactorily rehabilitated, remedial

seepage control facilities should be installed (see Chapter 12). The majority

of rehabilitation of seepage control facilities is in connection with relief

wells. Often a relief well does not flow except during high reservoir levels.

The water in the well becomes stagnant, various chemicals precipitate, algae

grows, and the efficiency of the well deteriorates. This will be manifested

by a fall in relief well discharge accompanied by a rise in piezometric

levels. Rehabilitation of a relief well is in essence a redevelopment of the

well. In addition to mechanical methods such as water jetting, surging, compressed air, and pumping, certain chemicals, detergents, and water softeners

can be used in the rehabilitation process.. Chemical tests on water samples

from the wells will indicate if and what chemicals are applicable. An examination of the well screen with a borehole TV camera is recommended, turbidity

of the water permitting, to determine the degree of deterloration and/or

clogging of the screen. For well screens constructed of metal (no wooden

screens) that will not be damaged by acid, incrustation from calcium carbonate

that has cemented gravel filter particles can be removed by treatment with

hydrochloric acid. For well screens constructed of metal, treatment with

chlorine can remove bacterial growths of slimes. Iron oxides may be removed

by treatment with polyphosphate and surging the well. Calcium hypochlorite

can be used with polyphosphates to kill iron bacteria (Johnson Division,

Universal Oil Products Co. 1972).

14-3
EM 1110-2-1901

30 Sep 86

APPENDIX A

REFERENCES

Government Publications

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

TM 5-818-5.

TM 5-545.

ER 1110-2-100.

ER 1110-2-101.

EM 1110-2-1901.

EM 1110-2-1902.

EM 1110-2-1905.

EM 1110-2-1906.

EM 1110-2-1908.

EM 1110-2-1911.

EM 1110-2-1913.

EM 1110-2-2300.

EM 1110-2-2400.

EM 1110-2-2501.

EM 1110-2-3501.

EM 1110-2-3506.

EM 1110-2-4000.

Albritton, J., Jackson, L., and Bangert, R., "Foundation Grouting Practices at Corps of Engineers Dams," TR GL-84-13, 1984, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Al-Hussaini, M., and Townsend, F. C., "Investigation of Tensile Strength

of Compacted Soils," Miscellaneous Paper S-74-10, Jun 1974, U. S. Army

Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS

39180-0631.

Banks, D. C., "Three-Dimensional Electrical Analogy Seepage Model

Studies; Appendix A: Flow to Circular Well Arrays Centered Inside a Circular Source, Series G," Technical Report No. 3-619, Mar 1963, U. S. Army

A-1
EM 1110-2-1901

30 Sep 86

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS

39180-0631.

Banks, D. C. "Three-Dimensional Electrical Analogy Seepage Model Studies;

Appendix B: Flow to a Single Well Centered Inside a Circular Source,

Series H," Technical Report No. 3-619, Mar 1965, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Bedinger, M. S., "Relationship Between Median Grain Size and Permeability

in the Arkansas River Valley, Arkansas," Professional Paper 424-C, 1961,

U. S. Department of the Interior, Geological Survey, 1717 H Street N.W.,

Washington, DC 20277.

Bureau of Reclamation, Groundwater Manual, Denver, Colo., 1977. Available from: Technical Information Center, U. S. Army Engineer/Waterways

Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Bureau of Reclamation, Water Measurement Manual, 2nd ed., 1967, U. S.

Department of the Interior, P. O. Box 25007, Denver, CO 80225.

Cedergren, H. R., "Flow Net Studies for Several Dams," for U. S. Army

Engineer District, Sacramento, Mar 1975, 650 Capitol Mall, Sacramento, CA

95814.

Clay, F. M., A Century on the Mississippi, A History of the Memphis

District, U. S. Army Corps of Engineers 1876-1876, Jan 1976, U. S. Army

Engineer District, Clifford Davis Federal Building, Memphis, TN 38103.

Clough, G. W., "An Evaluation of the Technical Feasibility of a Slurry

Trench Cutoff for the Excavation for the Tensas-Cocodrie Pumping Plant,

and a Review of Slurry Trench Specifications," 1978, report prepared for

U. S. Army Engineer District, P. O. Box 60, Vicksburg, MS 39180.

Cobb, J. E., "Seepage Analysis Report - Stage 3, Specifications, Calamus

Dam, Nebraska," Technical Memorandum No. V-222-B-lg, Jan 1984, Bureau of

Reclamation, P. O. Box 25007, Denver, CO 80225.

Cooley, R. L., Harsh, J. F., and Lewis, D. C., "Principles of GroundWater Hydrology," Hydrologic Engineering Methods for Water Resources

Development, Vol 10, Apr 1972, U. S. Army Engineer Hydrologic Engineering

Center, 609 Second Street, Davis, CA 95616.

Cooper, S. S., and Bieganousky, W. A., "Geophysical Survey of Cavernous

Areas, Patoka, Indiana," Miscellaneous Paper S-78-1, Jan 1978, U. S. Army

Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS

39180-0631.

Cooper, S. S., Koester, J. P., and Franklin, A. G., "Geophysical Investigation at Gathwright Dam," Miscellaneous Paper GL-82-2, Mar 1982, U. S.

Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS

39180-0631.

A-2
EM 1110-2-1901

30 Sep 86

32. Desai, C. S., "Seepage in Mississippi River Banks, Analysis of Transient

Seepage Using a Viscous-Flow Model and Finite Difference and Finite Element Methods," Technical Report S-73-S, Report 1, May 1973, U. S. Army

Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS

39180-0631.

33. Desai, C. S., "Seepage in Mississippi River Banks; Analysis of Transient

Seepage Using Viscous Flow Model and Numerical Methods," Miscellaneous

Paper S-70-3, Report 1, Feb 1970, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

34. Desai, C. S., and Kuppusamy, T., "Development of Phreatic Surfaces in

Earth Embankments," report prepared for the Bureau of Reclamation, May

1980, Department of Civil Engineering, Virginia Polytechnic Institute,

Blacksburg, Va. Available from: Technical Information Center, U. S.

Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS

39180-0631.

35. Duncan, J. M., "Seepage Analysis for Columbia Lock and Dam," Miscellaneous Paper No. 3-503, Jun 1962, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

36. Duncan, J. M., "Three-Dimensional Electrical Analogy Seepage Model

Studies," Technical Report No. 3-619, Mar 1963, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

37. Edris, E. V., Jr., and Vanadit-Ellis, W., "Geotechnical Computer Program

Survey," Miscellaneous Paper GL-82-1, Mar 1982, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

38. Environmental Protection Agency, "Manual of Methods for Chemical Analysis

of Water and Wastes," EPA-625-6-76-003a, Jul 1976, 26 W. St. Clair

Street, Cincinnati, OH 45268.

39. Franke, P., "The Concrete-Pile Cutoff Wall According to the I.C.O.S. -

Vedner Patent," Translation No. 54-6, Sep 1954, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

40. Gerwick, B. C., Jr., Holland, T. C., and Komendant, G. J., "Tremie Concrete for Bridge Piers and Other Massive Underwater Placements," Report

No. FHWA-RD-81-153, Sep 1981, U.S. Department of Transportation, Federal

Highway Administration, Washington, D. C. Available from: Technical

Information Center, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

41. Guertin, J. D., and McTigue, W. H., "Groundwater Control Systems for

Urban Tunneling," Groundwater Control in Tunneling, Vol 1, Report

No. FHWA-RD-81-073, Apr 1982, U. S. Department of Transportation, Federal

Highway Administration, Washington, D. C. Available from: Technical

Information Center, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

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42.

43.

44.

45.

46.

47.

48.

49.

50.

51.

Hall, R. L., Tracy, F. T., and Radhakrishnan, N. "Documentation of Twoand Three-Dimensional Seepage Problems Using the Finite Element Method,"

Miscellaneous Paper No. K-75-6, Jun 1975, U. S. Army Engineer Waterways

Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Hallford, C. R., "Fluid Trench Construction, Concrete Diaphragm Wall Construction," Lecture for Construction of Earth and Rockfill Dams Course,

Mar 1983, U. S. Army Engineer Waterways Experiment Station, P. O.

Box 631, Vicksburg, MS 39180-0631.

Hanson, J. E., "Impervious Cutoff by Means of Slurry Trench Construction

Mill Site Dam and Reservoir, Ferron Creek, Ferron Utah," 1972, U. S.

Department of Agriculture, Soil Conservation Service, P. O. Box 11350,

Salt Lake City, UT 84147.

Harza Engineering Company, "Engineering Investigations and Design Studies

for Underseepage Control (Slurry Trench Cutoff) for Saylorville Dam, Des

Moines River, Iowa," Nov 1965, report prepared for U. S. Army Engineer

District Clock Tower Building, Rock Island, IL 61201.

Hem, J. D., "Study and Interpretation of the Chemical Characteristics of

Natural Water," Water-Supply Paper No. 1473, 1970, U. S. Department of

Interior Geological Survey, 1717 H Street, Washington, DC 20277.

Holland, T. C., and Turner, J. R., "Construction of Tremie Concrete Cutoff Wall, Wolf Creek Dam, Kentucky," Miscellaneous Paper SL-80-10, Sep

1980, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

Jansen, R. B., Dams and Public Safety, 1980, U. S. Department of the

Interior, Bureau of Reclamation, Denver Federal Center, Denver, CO

80225.

Kealy, C. D., and Busch, R. A., "Determining Seepage Characteristics of

Mill-Tailings Dams by the Finite Element Method," Report of Investigations 7477, Jan 1971, U. S. Bureau of Mines, Spokane Mining Research

Center, Spokane, Wash. Available from: Technical Information Center,

U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

Koester, J. P., et al, "Geophysical Investigations in Support of Clearwater Dam Comprehensive Seepage Analysis," Miscellaneous Paper GL-84-3,

May 1984, U. S. Army Engineer Waterways Experiment Station, P. O.

Box 631, Vicksburg, MS 39180-0631.

Leach, R. E., "Waterbury Dam Seepage Study," draft report prepared for

U. S. Army Engineer District, New York, 1982, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

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55.

56.

57.

58.

59.

60.

61.

62.

Lohman, S. W., et al., "Definition of Selected Ground-Water Terms -

Revisions and Conceptual Refines," Water-Supply Paper 1988, 1972, U. S.

Department of the Interior, Geological Survey, 1717 H Street, Washington,

DC 20277.

Mansur, C. I., and Perret, W. R., "Efficacy of Partial Cutoffs for Controlling Underseepage Beneath Levees," Technical Memorandum No. 3-267,

Jan 1949, U. S. Army Engineer Waterways Experiment Station, P. O.

Box 631, Vicksburg, MS 39180-0631.

Mantei, C. L., and Cobb, J. E., "Seepage Analysis, Progress Report -

Stage 2, Specifications, Calamus Dam, Nebraska," Technical Memorandum

No. V-222-B-1-F, 1981, Bureau of Reclamation, P. O. Box 25007, Denver, CO

80225.

Mantei, C. L., Esmiol, E. E., and Cobb, J. E., "Seepage Analysis, Calamus

Dam - Stage I, Pick-Sloan Missouri River Basin Project, Nebraska,"

Technical Memorandum No. V-224-A, Mar 1980, Bureau of Reclamation, P. O.

Box 25007, Denver, CO 80225.

McAnear, C. L., and Trahan, C. C., "Three-Dimensional Seepage Model

Study, Oakley Dam, Sangamon River, Illinois," Miscellaneous Paper S-72-3,

Jan 1972, U. S. Army Engineer Waterways Experiment Station, P. O.

Box 631, Vicksburg, MS 39180-0631.

Miller, S. P., "Geotechnical Containment Alternatives for Industrial

Waste Basin F Rocky Mountain Arsenal Denver, Colorado; A Quantitative

Evaluation," Technical Report GL-79-23, Sep 1979, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Montgomery, R. L., "Investigation of Relief Wells, Mississippi River

Levees, Alton to Gale, Illinois," Miscellaneous Paper S-72-21, Jun 1972,

U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

Moser, J. H., and Huibregtse, K. R., "Handbook for Sampling and Sample

Preservation of Water and Wastewater," EPA-600-4-76-049, Sep 1976,

Environmental Protection Agency, 26 W. St. Clair Street, Cincinnati, OH

45268.

Nettles, E. H., and Calhoun, C. C., "Drainage Characteristics of Base

Course Materials, Laboratory Investigation," Technical Report No. 3-786,

Jul 1967, U. S. Army Engineer Waterways Experiment Station, P. O.

Box 631, Vicksburg, MS 39180-0631.

Nobari, E. S., Lee, K. L., and Duncan, J. M., "Hydraulic Fracturing in

Zoned Earth and Rockfill Dams," Contract Report CR S-73-2, Jan 1973,

U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

Pace, M. E., et al., "Seepage Analysis of Confined Flow Problems by the

Method of Fragments," Instruction Report K-84-8, Sep 1984, U. S. Army

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Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS

39180-0631.

63. Perry, E. B., "Laboratory Tests on Granular Filters for Embankment Dams,"

Draft Technical Report, 1986, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

64. Perry, E. B., "Piping in Earth Dams Constructed of Dispersive Clay;

Literature Review and Design of Laboratory Tests," Technical Report

No. S-75-15, Nov 1975, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

65. Perry, E. B., "Susceptibility of Dispersive Clay at Grenada Dam,

Mississippi, to Piping and Rainfall Erosion," Technical Report

No. GL-79-14, Sep 1979, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

66.

67.

68.

69.

70.

71.

72.

73.

Radhakrishnan, N., "Flow Nets and Computer Solutions to Seepage

Problems," Seminar on Construction Dewatering and Pressure Relief,

Jan-Feb 1978, U. S. Army Engineer Waterways Experiment Station, P. O.

Box 631, Vicksburg, MS 39180-0631.

Sherard, J. L., "Filters for Glacial Tills and Other Coarse Impervious

Soils," Memorandum IG, May 1984, Soil Conservation Service Soil Mechanics

Laboratory, Lincoln, Nebraska. Available from: Technical Information

Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

Soil Conservation Service, "Ground Water," National Engineering Handbook,

Section 18, Jun 1978, U. S. Department of Agriculture, P. O. Box 2890,

Washington, DC 20013.

Spooner, P. A., et al., "Technical Handbook on Slurry Trench Construction

for Pollution Migration Control," EPA draft, Oct 1982, U. S. Environmental Protection Agency, 26 W. St. Clair Street, Cincinnati, OH 45268.

Stanley Consultants, Inc., and Woodward-Clyde Consultants, "Lake Chicot

Pumping Plant, Inspection Guidelines for Slurry Trench Construction," Sep

1976, prepared for U. S. Army Engineer District, P. O. Box 60, Vicksburg,

MS 39180-0631.

Stanley Consultants, Inc., and Woodward-Clyde Consultants, "Lake Chicot

Pumping Plant, Letter Report, Slurry Trench," Apr 1977, U. S. Army

Engineer District, P. O. Box 60, Vicksburg, MS 39180-0631.

Talbot, J. R., and Nelson, R. E., "The Mechanics of Seepage Analysis,"

Soil Mechanics Note No. 7, Oct 1979, U. S. Department of Agriculture,

Soil Conservation Service, P. O. Box 2890, Washington, DC 20013.

Tracy, F. T., "An Interactive Graphics Finite Element Method Grid Generator for Two-Dimensional Problems," Miscellaneous Paper K-77-5, Aug 1977a,

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77.

78.

79.

80.

81.

82.

83.

84.

U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

Tracy, F. T., "An Interactive Graphics Postprocessor for Finite Element

Method Results," Miscellaneous Paper K-77-4, Aug 1977b, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS

39180-0631.

Tracy, F. T., "A Plane and Axisymmetric Finite Element Program for

Steady-State and Transient Seepage Problems," Miscellaneous Paper K-73-4,

May 1973a, U. S. Army Engineer Waterways Experiment Station, P. O.

Box 631, Vicksburg, MS 39180-0631.

Tracy, F. T., "A Three-Dimensional Finite Element Program for Steady-State

and Transient Seepage Problems," Miscellaneous Paper K-73-3, May 1973b,

U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

U. S. Army Corps of Engineers, "Foundation Pumping Tests," Civil Works

Engineer Letter 63-16, 4 Dec 1963, Washington, D. C. Available from:

Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

U. S. Army Engineer District, Baltimore, "Susquehanna River Basin, Kettle

Creek, Pennsylvania, Kettle Creek Reservoir, Embankments," Design

Memorandum No. 7, Oct 1958, P. O. Box 1715, Baltimore, MD 21203.

U. S. Army Engineer District, Baltimore, "Susquehanna River Basin, TiogaHammond Lakes, Tioga River and Crooked Creek, Pennsylvania, Instrumentation and Inspection," Design Memorandum No. 19, Jun 1973, P. O. Box 1715,

Baltimore, MD 21203.

U. S. Army Engineer District, Ft. Worth, "Brazos River Basin, Aquilla

Creek, Texas, Aquilla Lake, Embankment, Spillway, and Outlet Works,"

Design Memorandum No. 7, May 1976a, P. O. Box 17300, Ft. Worth, TX 76102.

U. S. Army Engineer District, Ft. Worth, "Trinity River Basin, Elm Fork,

Trinity River, Aubrey Lake, Texas, Embankment and Spillway (Revised),"

Design Memorandum No. 5, Jun 1976b, P. O. Box 17300, Ft. Worth, TX 76102.

U. S. Army Engineer District, Ft. Worth, "Trinity River Basin, Mountain

Creek, Lakeview Lake, Texas, Embankment and Spillway," Design Memorandum

No. 9, Apr 1980, P. O. Box 17300, Ft. Worth, TX 76102.

U. S. Army Engineer District, Galveston, "Buffalo Bayou and Tributaries,

Addicks and Barker Dams, Texas, Emergency Seepage Control, Construction

Completion Report," Jan 1983, P. O. Box 1229, Galveston, TX 77553.

U. S. Army Engineer District, Galveston, "Buffalo Bayou and Tributaries,

Addicks Dam, Texas," Inspection Report No. 3, 1977a, P. O. Box 1229,

Galveston, TX 77553.

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85.

86.

87.

88.

89.

90.

91.

92.

93.

94.

95.

96.

97.

U. S. Army Engineer District, Galveston, "Buffalo Bayou and Tributaries,

Texas, Addicks Dam, Letter Report for Emergency Seepage Control," May

1977b, P. O. Box 1229, Galveston, TX 77553.

U. S. Army Engineer District, Galveston, "Buffalo Bayou and Tributaries,

Texas, Major Rehabilitation, Addicks and Barker Dams," Reconnaissance

Report, 1977c, P. O. Box 1229, Galveston, TX 77553.

U. S. Army Engineer District, Huntington, "Kokosing River Basin, North

Branch of Kokosing Dam and Reservoir," Design Memorandum No. 5, Vol 1, Feb

1969, 502 Eighth Street, Huntington, WV 25701.

U. S. Army Engineer District, Huntington, "Muskingum River Watershed,

Bolivar Dam, Sandy Creek/Ohio," Embankment Reanalysis Report, Vol 1, Sep

1979a, 502 Eighth Street, WV 25701.

U. S. Army Engineer District, Huntington, "Muskingum River Watershed,

Mohawk Dam, Walhonding River, Ohio," Embankment Reanalysis Report, Vol 1,

Dec 1979b, 502 Eighth Street, Huntington, WV 25701.

U. S. Army Engineer District, Kansas City, "Hillsdale Lake, Osage River

Basin, Big Bull Creek, Kansas," Plans for Hillsdale Dam, Apr 1978,

601 E. 12th Street, Kansas, City, MO 64106.

U. S. Army Engineer District, Kansas City, "Long Branch Lake, Chariton

River Basin, East Fork Little Chariton River, Missouri," Jul 1974,

601 East 12th Street, Kansas City, MO 64106.

U. S. Army Engineer District, Little Rock, "Laboratory Technical

Memorandum for Construction and Use of Flow Nets," Sep 1940,

P. O. Box 867, Little Rock, AR 72203.

U. S. Army Engineer District, Los Angeles, "Painted Rock Reservoir, Gila

River, Arizona, Seepage Control Measures," Oct 1981, P. O. Box 2711, Los

Angeles, CA 90053.

U. S. Army Engineer District, Louisville, "Taylorsville Lake, Ohio River

Basin, Salt River, Kentucky, Dam and Spillway," Design Memorandum No. 6,

Jan 1974, P. O. Box 59, Louisville, KY 60201.

U. S. Army Engineer District, Memphis, "Foundation Report, Design, Construction, and Performance of the Impervious Cutoff at W. G. Huxtable

Pumping Plant, Marianna, Arkansas," Apr 1978, Clifford Davis Federal

Building, Memphis, TN 38103.

U. S. Army Engineer District, Mobile, "Carters Dam, Coosawattee River,

Georgia, Embankment Criteria and Performance Report," Mar 1976,

P. O. Box 2288, Mobile, AL 36628.

U. S. Army Engineer District, Mobile, "Okatibbee Dam, Okatibbee Creek,

Mississippi, Main Dam and Spillway," Design Memorandum No. 8, Apr 1965,

P. O. Box 2288, Mobile AL 36628.

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98. U. S. Army Engineer District, Nashville, "Wolf Creek Dam, Cumberland

River, Kentucky, Concrete Diaphragm Walls, Plans and Specifications,

Phase 1," Apr 1975, P. O. Box 1070, Nashville, TN 37202.

99. U. S. Army Engineer District, Omaha, "Embankment Criteria and Performance Report, Missouri River, Fort Peck Lake, Montana," Vol I, Sep 1982,

215 N. 17th Street, Omaha, NE 68102.

100. U. S. Army Engineer District, Omaha, "Missouri River, Oahe Reservoir,

South Dakota, Relief Wells," Design Memorandum No. MO-162, Nov 1961,

215 N. 17th Street, Omaha, NE 68102.

101. U. S. Army Engineer District, Omaha, "Report on Underseepage Observations, Garrison Dam," May 1964, 215 N. 17th Street, Omaha, NE 68102.

102. U. S. Army Engineer District, Philadelphia, "Lehigh River Basin, Jordan

Creek, Pennsylvania, Trexler Lake, Embankment, Spillway and Outlet

Works," Design Memorandum No. 7, Nov 1974, US Custom House 2nd and

Chestnut Streets, Philadelphia, PA 19106.

103. U. S. Army Engineer District, Pittsburgh, "Upstream Concrete Cut-Off

Wall, Allegheny Reservoir Dam," Cut-Off Wall Construction, Part II, Jul

1965, 1000 Liberty Avenue, Pittsburgh, PA 15222.

104. U. S. Army Engineer District, Portland, "Applegate Lake, Applegate

River, Oregon, Instrumentation, Inspection, and Evaluation," Design

Memorandum No. 15, Apr 1978, P. O. Box 2946, Portland, OR 97208.

105. U. S. Army Engineer District, Rock Island, "Local Flood Protection Project, Rockford - Stage I, Kent Creek, Winnebago County, Illinois,"

Specifications for Page Park Dam, Jun 1978a, Clock Tower Building, Rock

Island, IL 61201.

106. U. S. Army Engineer District, Rock Island, "Slurry Trench Cutoff, DamFoundation Report, Saylorville Lake, Des Moines River, Iowa," Part VI,

Binder 3 of 5, Jan 1978b, Clock Tower Building, Rock Island, IL 61201.

107. U. S. Army Engineer District, Sacramento, "Buchanan Dam, H. V. Eastman

Lake, Chowchilla River, California, Embankment Criteria and Performance

Report," Apr 1977, 650 Capitol Mall, Sacramento, CA 95814.

108. U. S. Army Engineer District, Savannah, "Construction of Slurry Trench

Cutoff," May 1968, P. O. Box 889, Savannah, GA 31402.

109. U. S. Army Engineer District, Savannah, "Specifications for Rehabilitation of Clemson Lower Division Dam, Hartwell Lake, Georgia and South

Carolina," Oct 1981, P. O. Box 889, Savannah, GA 31402.

110. U. S. Army Engineer District, Savannah, "West Point Dam, Chattahoochee

River, Alabama and Georgia, Embankment Criteria and Performance Report,"

Oct 1979, P. O. Box 889, Savannah, GA 31402.

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111. U. S. Army Engineer District, St. Louis, "Clarence Cannon Dam and

Reservoir, Upper Mississippi River Basin, Salt River, Missouri, Embankment Design, Main Dam," Design Memorandum No. 12, Nov 1969, 210 Tucker

Boulevard, St. Louis, MO 63101.

112. U. S. Army Engineer District, St. Louis, "John H. Overton Lock and Dam,

Red River Waterway," Design Memorandum No. 17, Detail Design, Vol 2,

Appendices, Design Computations, Nov 1978, St. Louis, MO. (prepared for

U. S. Army Engineer District, New Orleans).

113. U. S. Army Engineer District, Tulsa, "Big Hill Lake, Big Hill Creek,

Kansas, Embankment, Outlet Works, and Spillway," Design Memorandum

No. 6, Oct 1975, P. O. Box 61, Tulsa, OK 74121-0061.

114. U. S. Army Engineer District, Tulsa, "El Dorado Lake, Walnut River,

Kansas, Embankment and Spillway," Design Memorandum No. 6, Jul 1974,

P. O. Box 61, Tulsa, OK 74121-0061.

115. U. S. Army Engineer District, Vicksburg, "Operation and Maintenance

Manual, Grenada Dam, Yalobusha River, Mississippi," 1977, P. O. Box 60,

Vicksburg MS 39180-0631.

116. U. S. Army Engineer District, Walla Walla, "Mills Creek Lake,

Washington, Storage Dam Rehabilitation," Design Memorandum No. 6, Feb

1980a, Building 602, City-County Airport, Walla Walla, WA 99362.

117. U. S. Army Engineer District, Walla Walla, "Storage Dam Rehabilitation,

Mill Creek Flood Control Project, Walla Walla, Washington, Plans and

Specifications," Sep 1980b, Building 602, City-County Airport, Walla

Walla, WA 99362.

118. U. S. Army Engineer Division, Ohio River, "Conference on Control of

Underseepage," Apr 1945, P. O. Box 1159, Cincinnati, OH 45201.

119. U. S. Army Engineer Waterways Experiment Station, "Analysis of

Piezometer and Relief Well Data, Arkabutla Dam," Technical Report

No. 3-479, Jun 1958, P. O. Box 631, Vicksburg/MS 39180-0631.

120. U. S. Army Engineer Waterways Experiment Station, "Investigation of

Underseepage and Its Control, Lower Mississippi River Levees," 2 Vols,

Technical Memorandum No. 3-424, Oct 1956a, P. O. Box 631, Vicksburg, MS

39180-0631.

121. U. S. Army Engineer Waterways Experiment Station, "Review of Soils

Design, Construction, and Prototype Analysis, Blakely Mountain Dam,

Arkansas," Technical Report No. 3-439, Oct 1956b, P. O. Box 631,

Vicksburg, MS 39180-0631.

122. U. S. Army Engineer Waterways Experiment Station, "The Unified Soil

Classification System," Technical Memorandum No. 3-357, Apr 1960, P. O.

Box 631, Vicksburg, MS 39180-0631.

A-10
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124

125

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30 Sep 86

U. S. Department of Agriculture, Soil Conservation Service, "Soil

Mechanics Note No. 5, Flow Net Construction and Use," Oct 1973, P. O.

Box 2890, Washington, DC 20013.

Warriner, J. B., and Banks, D. C., "Numerical Analysis of Partially

Penetrating Random Well Arrays," Technical Report S-77-5, 1977, U. S.

Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS

39180-0631.

Weeks, E. P., "Field Determination of Vertical Permeability to Air in

the Unsaturated Zone," U.S.G.S. Professional Paper 1051, 1978, U. S.

Geological Survey, National Center, 12201 Sunrise Valley Drive, Reston,

VA 22092.

126. Winter, C. D., "Design of Slurry Trenches on the Tennessee-Tombigbee

Waterway," paper presented at the CE Seminar on Design and Construction

of Slurry Trenches on Tennessee-Tombigbee Waterway, Tupelo, Miss., Aug

1978. Available from: Technical Information Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS

39180-0631.

127. Zangar, C. N., "Theory and Problems of Water Percolation," Engineering

Monograph No. 8, Apr 1953, Bureau of Reclamation, Denver, Colo. Available from: Technical Information Center, U. S. Army Engineer Waterways

Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

128. Zeigler, T. W., "Determination of Rock Mass Permeability," Technical

Report S-76-2, Jan 1976, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Non-Government Publications

129.

130.

131.

132.

Ambraseys, N. N., "Cut-Off Efficiency of Grout Curtains and Slurry

Trenches," Grouts and Drilling Muds in Engineering Practice,

Butterworths, London, 1963, pp 43-46. Available from: Technical

Information Center, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

American Petroleum Institute, "Oil-Well Drilling Fluid Materials,"

Specification No. 13A, 8th ed., Mar 1981, Dallas, Tex. Available from:

American Petroleum Institute, 211 North Ervay, Suite 1700, Dallas, TX

75201.

American Petroleum Institute, "Standard Procedure for Testing Drilling

Fluids," Recommended Practice No. 13B, 9th ed., May 1982, Dallas, Tex.

Available from: American Petroleum Institute, 211 North Ervay,

Suite 1700, Dallas, TX 75201.

Anonymous, "Fast Value Engineering Saves Over Budget Dam," Engineering

News Record, Vol 201, No. 19, 9 Nov 1978, pp 24-25. Available from:

Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

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133.

134.

135.

136.

137.

138.

139.

140.

141.

142.

Anonymous, "Ground Water: Our Priceless Resource," Ground Water Age,

Vol 14, No. 8, Apr 1980, pp 33-36, 64-66. Available from: Technical

Information Center, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

Anonymous, "World's Deepest Cutoff Wall Reaches 430 Ft," Engineering

News Record, Vol 188, No. 1, 6 Jan 1972, pp 26-28. Available from:

Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Anton, W. F., and Dayton, D. J., "Comanche Dike-2 Slurry Trench Seepage

Cutoff," Proceedings-of the Conference on Performance of Earth and

Earth-Supported Structures, Purdue University, Vol 1, Part 1, 1972,

pp 735-749. Available from: Technical Information Center, U. S. Army

Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS

39180-0631.

Arulanandan, K., and Perry, E. B., "Erosion in Relation to Filter Design

Criteria for Earth Dams," Journal of the Geotechnical Engineering

Division, American Society of Civil Engineers, Vol 109, No. 5, May 1983,

pp 682-698. Available from: Technical Information Center, U. S. Army

Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS

39180-0631.

Barber, E. S., and Sawyer, C. L., "Highway Subdrainage," Proceedings,

Highway Research Board, 1952, pp 643-666. Available from: Technical

Information Center, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

Barron, R. A., "The Design of Earth Dams," Handbook of Dam Engineering,

A. R. Golze, ed., Van Nostrand, New York, 1977, pp 291-318. Available

from: Technical-Information Center, U. S. Army Engineer Waterways

Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Basak, P., and Madhav, M. R., "Upper and Lower Limit of Darcy's Law,"

Indian Geotechnical Journal, Vol 9, No. 2, Apr 1979, pp 134-153.

Available from: Technical Information Center, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Bear, J., Dynamics of Fluids in Porous Media, Elsevier, New York, 1972.

Available from: Technical Information Center, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Blind, H., "Inspection Galleries in Earth and Rockfill Dams," Water

Power and Dam Construction, Vol 34, No. 4, Apr 1982, pp 25-31. Available from: Technical Information Center, U. S. Army Engineer Waterways

Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Bloom, E., Dynes, S., and Glossett, C., "Soil Bentonite Slurry Trench in

a PL-566 Rolled Earth Dam in Indiana," Paper No. 79-2579 presented at

American Society of Agricultural Engineers Meeting, New Orleans, La.,

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143. Boer, S. A. De, and Molen, W. H. Van Der, "Electrical Models: Conductive Sheet Analogies," Drainage Principles and Applications, International Institute for Land Reclamation and Improvement, Wageningen,

Netherlands, Publication 16, Vol 1, 1972, pp 201-221. Available from:

Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

144. Bourdeaux, G. and Imaizumi, H., "Dispersive Clay at Sobradinho Dam,"

Dispersive Clays, Related Piping, and Erosion in Geotechnical Projects,

Special Technical Publication 623, May 1977, pp 13-24. American Society

for Testing and Materials, Philadelphia, Penn, Available from: Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

145. Brand, E. W., and Armstrong, R., "Sand Model Studies of Seepage Through

Earth Dams," Proceedings, Symposium on Earth and Rockfill Dams, Indiana,

Vol 1, 1968, pp 188-196. Available from: Technical Information Center,

U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

146. Bros, B., and Orzeszyna, H., "The Influence of Particle Angularity and

Surface Roughness on Engineering Properties of Sand," Design Parameters

in Geotechnical Engineering, British Geotechnical Society, London, 1979,

pp 11-14. Available from: Technical Information Center, U. S. Army

Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS

39180-0631.

147. Burmister, D. M., "Principles of Permeability Testing of Soils,"

Symposium on Permeability of Soils, ASTM Special Technical Publication

No. 163, American Society for Testing and Materials, Apr 1955, pp 3-26.

Available from: Technical Information Center, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

148. Burmister, D. M., "The Importance and Practical Use of Relative Density

in Soil Mechanics," Proceedings, American Society for Testing and

Materials, Vol 48, 1948, pp 1249-1268. Available from: Technical

Information Center, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

149.

150.

Cary, A. S., Walter, B. H., and Horstad, H. T., "Permeability of Mud

Mountain Dam Core Material," Transactions, American Society of Civil

Engineers, Vol 108, 1943, pp 719-737. Available from: Technical

Information Center, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

Casagrande, A., "Control of Seepage Through Foundations and Abutments of

Dams," Geotechnique, Vol 11, No. 3, 1961, pp 161-182. Available from:

Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

1979. Available from: American Society of Agricultural Engineers, P. O.

Box 229, St. Joseph, MI 49085.

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151. Casagrande, A., "Seepage Through Dams," New England Waterworks Association, Vol LI, No. 2, Jun 1937, Dedham, Mass. Available from: Technical

Information Center, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

152. Case International Company, "Case Slurry Wall Notebook," 1982, Roselle,

Ill. Available from: Case International Company, P. O. Box 40,

Roselle, IL 60172.

153. Cedergren, H. R., "Drainage and Dewatering," Foundation Engineering

Handbook, H. F. Winterkorn and H.-Y. Fang, eds., Van Nostrand Reinhold,

New York, 1975, pp 221-243. Available from: Technical Information

Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

154. Cedergren, H. R., "Seepage Control in Earth Dams," Embankment-Dam

Engineering, R. C. Hirschfield and S. J. Poulos, eds., Wiley, New York,

1973, pp 21-45. Available from: Technical Information Center, U. S.

Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS

39180-0631.

155. Cedergren, H. R., Seepage, Drainage and Flow Nets, 2nd ed., Wiley, New

York, 1977. Available from: Technical Information Center, U. S. Army

Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg,

MS 39180-0631.

156. Christian, J. T., "Flow Nets by the Finite Element Method," Ground

Water, Vol 18, No. 2, Mar-Apr 1980a, pp 178-181. Available from:

Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

157. Christian, J. T., "Flow Nets from Finite Element Data," International

Journal for Numerical and Analytical Methods in Geomechanics, Vol 4,

Apr-Jun 1980b, pp 191-196. Available from: Technical Information

Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

158. Chugaev, R. R., "Seepage Through Dams," Advances in Hydroscience,

V. T. Chow, ed., Academic Press, New York, Vol 7, 1971, pp 283-325.

Available from: Technical Information Center, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

159. Coffman, J. A., Jr., and Franks, L. W., "Rehabilitating the Muskingum

River System," Transactions of the Fourteenth International Congress on

Dams, Q52 R.50, Rio de Janeiro, Brazil, 1982, pp 827-845. Available

from: Technical Information Center, U. S. Army Engineer Waterways

Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

160. Couch, F. B., and Ressi deCervia, A. L., "Seepage Cutoff Wall Installed

Through Dam is Construction First," Civil Engineering, American Society

of Civil Engineers, Vol 49, No. 1, Jan 1979, pp 62-66. Available from:

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Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

161. Coxon, R. E., and Crook, D. E., "Some Simple Approaches to Leakage

Detection in Dams," Transactions of the Twelfth International Congress

on Large Dams, Vol II, 1976, Mexico City, pp 527-540. Available from:

Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

162. Dank, A. I., The Influence of Sand on the Engineering Properties of

Cement Bentonite Slurry Used for Cut-off Walls, M.S. Thesis, Aug 1981,

Northwestern University, Evaston, Ill. Available from: Technical

Information Center, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

163. D'Appolonia, D. J., "Soil-Bentonite Slurry Trench Cutoffs," Journal of

the Geotechnical Engineering Division, Vol 106, No. GT4, Apr 1980,

American Society of Civil Engineers, New York. Available from: Technical Information Center, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

164. Davis, S. N., and Dewiest, R. J. M., Hydrogeology, Wiley, New York,

1966. Available from: Technical Information Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg,

MS 39180-0631.

165. Denny, K. J., Grain Size Distribution and Its Effect on the Permeability

of Unconsolidated Sands, M.S. Thesis, 1965, University of Texas, Austin,

Tex. Available from: Technical Information Center, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

166. Desai, C. S., "Flow Through Porous Media," Numerical Methods in

Geotechnical Engineering, C. S. Desai, and J. T. Christian, eds.,

McGraw-Hill, New York, 1977, pp 458-505. Available from: Technical

Information Center, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

167. Desai, C. S., and Abel, J. F., Introduction to the Finite Element

Method, Van Nostrand Reinhold, New York, 1972. Available from:

Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

168. Duguid, D. R., et al., "The Slurry Trench Cut-Off for the Duncan Dam,"

Canadian Geotechnical Journal, Vol 8, No. 1, Feb 1971, pp 94-108.

Available from: Technical Information Center, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

169. Dvinoff, A. H., Response of the Phreatic Surface in Earthen Dams to

Headwater Fluctuations, Ph. D. Thesis, 1970, Purdue University, West

Lafayette, Ind. Available from: Technical Information Center, U. S.

Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS

39180-0631.

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170.

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179.

Eisenstein, Z., "Computer Analyses in Earth Dam Engineering," Computers

in Soil Mechanics: Present and Future, R. L. Schiffman, ed., MAA

Publishing Co., Taipei, 1979, pp 79-122. Available from: Technical

Information Center, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

Fenn, C. D., The Effects of Montmorillonite and Kaolinite Dispersions on

the Permeability of a Porous Media, M.S. Thesis, 1966, Mississippi State

University, State College, Miss. Available from: Technical Information

Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

Fetter, C. W., Jr. Applied Hydrology, Charles E. Merrill, Columbus,

Ohio, 1980. Available from: Technical Information Center, U. S. Army

Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS

39180-0631.

Fetzer, C. A., "Wolf Creek Dam - Remedial Work, Engineering Concepts

Actions, and Results," Transactions of the Thirteenth International

Congress on Large Dams, Vol 2, 1979, New Delhi, India, pp 57-82.

Available from: Technical Information Center, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Forcheimer, P. H., Hydraulik, Teubner, Berlin, 1914. Available from:

Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Freeze, R. A., and Cherry, J. A., Groundwater, Prentice-Hall, New York,

1979. Available from: Technical Information Center, U. S. Army

Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS

39180-0631.

Fuquay, G. A,, "Foundation Cutoff Wall for Allegheny Reservoir Dam,"

Closure to discussion, Journal of the Soil Mechanics and Foundations

Division, pp 1363-1366, American Society of Civil Engineers, New York,

Vol 94, No. SM6, Nov 1968. Available from: Technical Information

Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

Gebhart, L. R. "Foundation Seepage Control Options for Existing Dams,"

Inspection, Maintenance and Rehabilitation of Old Dams, American Society

of Civil Engineers, New York, 1974, pp 660-676. Available from:

Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Greer, D. M., Moorhouse, D. C., and Millet, R. A., "Sheet Pile Interlock

Seepage Study," Woodward-Moorhouse & Associates, Inc., New York, 1969.

Available from: Woodward-Clyde & Associates, Inc., Two Pennsylvania

Plaza, New York, NY 10001.

Hanna, T. H., "Diaphragm Walls," Developments in Soil Mechanics,

C. R. Scott, ed., Applied Science, London, 1978, pp 213-249. Available

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30 Sep 86

from: Technical Information Center, U. S. Army Engineer Waterways

Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

180. Harr, M. E., Groundwater and Seepage, McGraw-Hill Book Company, New

York, 1962. Available from: Technical Information Center, U. S. Army

Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS

39180-0631.

181. Harr, M. E., Mechanics of Particulate Media, McGraw-Hill, New York,

1977. Available from: Technical Information Center, U. S. Army

Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS

39180-0631.

182. ICOS, "The ICOS Company in Underground Works," Vol 3, 1968, Milano,

Italy. Available from: ICOS Corporation of America, Four West 58th

Street, New York, NY 10019.

183. Isaacs, L. T., "Adjustment of Phreatic Line in Seepage Analysis by Finite

Element Method," Research Report No. CE2, Mar 1979, Department of Civil

Engineering, University of Queensland, Australia. Available from:

Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

184. Isaacs, L. T., "Location of Seepage Free Surface in Finite Element

Analyses," Transactions, Institution of Engineers, Australia, Vol CE22,

No. 1, Feb 1980, pp 9-16. Available from: Technical Information

Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

185. Jacob, C. E., "Flow of Groundwater," Engineering Hydraulics, H. Rouse,

ed., Wiley New York, 1950, p 346. Available from: Technical Information

Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

186. Jansen, R. B., "Engineering of Earth and Rockfill Dams in California,"

presented at Recent Developments in the Design and Construction of Earth

and Rockfill Dams, Mar 1968, University of California, Berkeley. Available from: Technical Information Center, U. S. Army Engineer Waterways

Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

187. Jefferis, S. A., "Bentonite-Cement Slurries for Hydraulic Cut-Offs,"

Proceedings, Tenth International Conference on Soil Mechanics and

Foundation Engineering, Stockholm, Sweden, Vol 1, 1981, pp 435-440.

Available from: Technical Information Center, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

188. Jenkins, J. D., and Bankofier, D. E., "Hills Creek Dam Seepage Correction," Performance of Earth and Earth-Supported Structures, American

Soceity of Civil Engineers, New York, 1972, pp 723-733. Available from:

Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

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Johnson Division, Universal Oil Products Co., Ground Water and Wells,

St. Paul, Minn., 1972. Available from: Technical Information Center, U.

S. Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg,

MS 39180-0631.

Jones, J. C., "Deep Cut-Offs in Pervious Alluvium Combining Slurry

Trenches and Grouting," Proceedings of the 9th International Congress on

Large Dams, Istanbul, Turkey, Vol 1, 1967, pp 509-524. Available from:

Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Jones, L. B., "Reservoir Seepage and Ground Water Control, McNary

Reservoirs," paper presented at the American Society of Civil Engineer

Convention, Phoenix, Ariz., 1961. Available from: Shannon & Wilson,

Inc., 1105 North 38th Street, Seattle, WA 98103.

Kaufman, R. I., "Effect of Top Stratum Permeability on Design of Seepage

Control Measures," In Situ Measurement of Soil Properties, North

Carolina State University, Vol II, 1976, pp 39-45. Available from:

Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Klohn, E. J., "Seepage Control for Tailings Dams," Mine Drainage,

G. O. Argall, Jr., ed., Miller Freeman Publications, San Francisco, 1979,

pp 671-725. Available from: Technical Information Center, U. S. Army

Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS

39180-0631.

Knabach, M. L., and Dingle, S. O., "Slurry Trench Cutoff in Dam

Construction," Paper No. 74-2014 presented at American Society of

Agricultural Engineers Meeting, Stillwater, Okla., 1974. Available

from: American Society of Agricultural Engineers, P. O. Box 229, St.

Joseph, MI 49085.

Koerner, R. M., Lord, A. E., Jr., and McCabe, W. M., "Acoustic Emission

(Microseismic) Monitoring of Earth Dams," The Evaluation of Dam Safety,

American Society of Civil Engineers, New York, 1977, pp 274-291.

Available from: Technical Information Center, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Kramer, H., "Deep Cutoff Trench of Puddled Clay for Earth Dam and Levee

Protection," Engineering News Record, Vol 136, No. 26, 27 Jun 1946,

pp 76-80. Available from: Technical Information Center, U. S. Army

Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS

39180-0631.

Krumbein, W. C., and Pettijohn, F. J., Manual of Sedimentary

Petrography, Appleton-Century Crofts, New York, 1938. Available from:

Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

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L ., Stratigraphy and Sedimentation,

1951. Available from: Technical Information Center, U. S. Army Engineer Waterways Experiment Station, P. O.

Box 631, Vicksburg, MS 39180-0631.

Kruseman, G. P., and DeRidder, N. A., "Analysis and Evaluation of Pumping Test Data," Bulletin 11, 1970, International Institute for Land

Reclamation and Improvement, Wageningen, Netherlands. Available from:

Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Lambe, T. W., Soil Testing for Engineers, Wiley, New York, 1951. Available from: Technical Information Center, U. S. Army Engineer Waterways

Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Lambe, T. W., and Whitman, R. V., Soil Mechanics, Wiley, New York, 1969.

Available from: Technical Information Center, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Lane, K. S., and Wohlt, P. E., "Performance of Sheet Piling and Blankets

for Sealing Missouri River Reservoirs," Transactions of the Seventh

International Congress on Large Dams, Vol 4, 1961, pp 25, Rome, Italy.

Available from: Technical Information Center, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

La Russo, R. S., "Wanapum Development - Slurry Trench and Grouted CutOff," Grouts and Drilling Muds in Engineering Practice, 1963,

pp 196-201, Butterworths, London. Available from: Technical Information Center, U. S. Army Engineer Waterways Experiment Station, P. O.

Box 631, Vicksburg, MS 39180-0631.

Lefebvre, G. C. L., Pare, J. J., and Tournier, J.-P., "Effectiveness of

Seepage Control Elements for Embankments on Semipervious Foundations,"

Canadian Geotechnical Journal, Vol 18, No. 4, Nov 1981, pp 572-576.

Available from: Technical Information Center, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Leonards, G. A., ed., Foundation Engineering, McGraw-Hill, New York,

1962. Available from: Technical Information Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg,

MS 39180-0631.

Leps, T. M., "Flow Through Rockfill," Embankment-Dam Engineering,

R. C. Hirschfield and S. J. Poulous, eds., Wiley, New York, 1973,

pp 87-107. Available from: Technical Information Center, U. S. Army

Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg,

MS 39180-0631.

Lewis, D. C., Kriz, G. J., and Burgy, R. H., "Tracer Dilution Sampling

Techniques to Determine Hydraulic Conductivity of Fractured Rock," Water

Resource Research, Vol 2, No. 3, 1966. Available from: Technical

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Ley, J. E. "Foundations of Existing Dams - Seepage Control," Inspection, Maintenance and Rehabilitation of Old Dams, American Society of

Civil Engineers, New York, 1974, pp 584-608. Available from: Technical

Information Center, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

Logani, K. L., and Lhez, M. H. H., "Dispersive Soils Used in the

Construction of the Ullum Dam in Argentina," Proceedings of the Sixth

Panamerican Conference on Soil Mechanics and Foundation Engineering,

Vol 111, Dec 1979, Lima, Peru, pp 394-411. Available from: Technical

Information Center, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

London, A. G., "The Computation of Permeability from Simple Soil Tests,"

Geotechnique, Vol 3, No. 4, 1952, pp 165-183. Available from: Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Louis, c., "A Study of Groundwater Flow in Jointed Rock and Its Influence

on the Stability of Rock Masses," Rock Mechanics Research Report No. 10,

1969, Imperial College, London, England. Available from: Technical

Information Center, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

Lovenbury, H. T., "The Detection of Leakage Through the Core of an

Existing Dam," Field Instrumentation in Geotechnical Engineering, Wiley,

1974, pp 240-248. Available from: Technical Information Center, U. S.

Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS

39180-0631.

Lowe, J., III. "Foundation Design - Tarbela Dam," The Fourth Nabor

Carrillo Lecture, Mexican Society for Soil Mechanics, Mexico, 1978.

Available from: Technical Information Center, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Lynch, E. J., Formation Evaluation, Harper and Row, New York, 1962.

Available from: Technical Information Center, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Maini, Y. N. T., In Situ Hydraulic Parameters in Jointed Rock: Their

Measurement and Interpretation, Ph. D. Dissertation, 1971, Imperial

College, London, England. Available from: Technical Information Center,

U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

Mansur, C. I,, and Dietrich, R. J., "Pumping Test to Determine

Permeability Ratio," Journal of the Soil Mechanics and Foundations

Division, Vol 91, No. SM4, Jul 1965, American Society of Civil Engineers, New York, pp 151-183. Available from: Technical Information

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Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

217. Mantei, C. L., and Harris, D. W., "Finite Element Seepage Analysis on

Reclamation Dams," Preprint 3691, paper presented at American Society of

Civil Engineers Convention and Exposition, Atlanta, Ga., Oct 1979.

Available from:. Technical Information Center, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

218. Marsal, R. J., and Resendiz, D., "Effectiveness of Cutoffs in Earth

Foundations and Abutments of Dams," Proceedings of the Fourth

Pan-American Conference on Soil Mechanics and Foundation Engineering,

Vol 1, Jun 1971, San Juan, Puerto Rico, pp 237-312. Available from:

Technical Information Center,, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

219. Masch, F. D., and Denny, K. J., "Grain Size Distribution and Its Effect

on the Permeability of Unconsolidated Sands," Water Resources Research,

Vol 2, No. 4, 1966, pp 665-677. Available from: Technical Information

Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

220. McDaniel, T. N., and Decker, R. S., "Dispersive Soil Problem at Los

Esteros Dam," Journal of the Geotechnical Engineering Division, Vol 105,

No. GT9, Sep 1979, pp 1017-1030, American Society of Civil Engineers,

New York. Available from: Technical Information Center, U. S. Army

Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg,

MS 39180-0631.

221. Meier, J. G., and Rettberg, W. Q., "Report on Cement-Bentonite Slurry

Trench Cutoff Wall: Filden Tailings Project," Tailings Disposal Today,

Vol 2, pp 341-365 , 1978, Miller Freeman Publications, San Francisco.

Available from: Technical Information Center, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

222. Miller, E. A., and Salzman, G. S., "Value Engineering Saves Dam Project," Civil Engineering, American Society of Civil Engineers, Vol 50,

No. 8, Aug 1980, pp 51-55. Available from: Technical Information

Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

223. Millet, R. A., and Perez, J.-Y., "Current USA Practice: Slurry Wall

Specifications," Journal of the Geotechnical Engineering Division,

American Society of Civil Engineers, Vol 107, No. GT8, Aug 1980,

pp 1041-1056. Available from: Technical Information Center, U. S. Army

Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS

39180-0631.

224. Milligan, V., "Field Measurement of Permeability in Soil and Rock," In

Situ Measurement of Soil Properties, American Society of Civil Engineers, New York, Vol 2, 1976, pp 3-36. Available from: Technical

A-21
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30 Sep 86

225.

226.

227.

228.

229.

230.

231.

232.

233.

Information Center, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

Missbach, A., "Listy Cukrovar," Vol 55, 1937, p 293, Prague,

Czechoslovakia. Available from: Technical Information Center, U. S.

Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS

39180-0631.

Mitchell, J. K., Fundamentals of Soil Behavior, Wiley, New York, 1976.

Available from: Technical Information Center, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Mitchell, J. K., Guzikowski, F., and Villet, W. C. B., "The Measurement

of Soil Properties In-Situ," Report No. LBL-6363, Mar 1978, Department

of Civil Engineering, University of California, Berkeley, Calif. Available from: Technical Information Center, U. S. Army Engineer Waterways

Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Morgenstern, N., and Amir-Tahmasseb, I., "The Stability of a Slurry

Trench in Cohesionless Soils," Geotechnique, Vol 15, No. 1, Dec 1965,

pp 387-395. Available from: Technical Information Center, U. S. Army

Engineer Waterways Experiment Station, P. Q. Box 631, Vicksburg,

MS 39180-0631.

Muskat, M., The Flow of Homogeneous Fluids Through Porous Media,

J. W. Edwards, Ann Arbor, Mich., 1946. Available from: Technical Information Center, U. S. Army Engineer Waterways Experiment Station, P. O.

Box 631, Vicksburg, MS 39180-0631.

Nash, J. K. T. L., "Slurry Trench Walls, Pile Walls, Trench Bracing,"

Proceedings, Sixth European Conference on Soil Mechanics and Foundation

Engineering, Vienna, Austria, Vol 2.1, 1976, pp 27-32. Available from:

Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Nash, J. K. T. L., and Jones, G. K., "The Support of Trenches Using

Fluid Mud," Grouts and Drilling Muds in Engineering Practice, 1963,

pp 177-180, Butterworths, London. Available from: Technical Information Center, U. S. Army Engineer Waterways Experiment Station, P. O.

Box 631, Vicksburg, MS 39180-0631.

Neuman, S. P. "Analysis of Pumping Test Data from Anisotropic Unconfined Aquifers Considering Delayed Gravity Response," Water Resource

Research, Vol 11, 1975, pp 329-342. Available from: Technical Information Center, U. S. Army Engineer Waterways Experiment Station, P. O.

Box 631, Vicksburg, MS 39180-0631.

Olson, R. E., and Daniel, D. E., "Field and Laboratory Measurement of

the Permeability of Saturated and Partially Saturated Fine-Grained

Soils," paper presented at the American Society for Testing and

Materials Symposium on Permeability and Groundwater Contaminant

Transport, Philadelphia, Pa., Jun 1979. Available from: Technical

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30 Sep 86

Information Center, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

234. Parker, D. G., and Thornton, S. I., "Permeability of Fly Ash and Fly Ash

Stabilized Soils," Dec 1976, Department of Civil Engineering, University

of Arkansas, Fayetteville, Ark. Available from: Technical Information

Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

235. Pavlovsky, N. M., Collected Works, 1956, Akad. Nauk USSR, Leningrad

(cited in Harr 1977). Available from: Technical Information Center,

U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

236. Pavlovsky, N. M., "Seepage Through Earth Dams," Instit. Gidrotekhniki i

Melioratsii, 1931, Leningrad, USSR, translated by U. S. Army Corps of

Engineers. Available from: Technical Information Center, U. S. Army

Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg,

MS 39180-0631.

237. Perloff, W. H., and Baron, W., Soil Mechanics, Ronald Press, New York,

1976. Available from: Technical Information Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg,

MS 39180-0631.

238. Pettyjohn, W. A,., et al., "A Ground-Water Quality Atlas of the United

States," May 1979, National Demonstration Water Project, Washington,

D. C. Available from: Technical Information Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg,

MS 39180-0631.

239. Polubarinova-Kochina, P. Ya., "Concerning Seepage in Heterogeneous

(Two-Layered) Media," Inzhenernii Sbornik, Vol 1, No. 2, 1941 (cited in

Harr 1977). Available from: Technical Information Center, U. S. Army

Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg,

MS 39180-0631.

240. Prickett, T. A., "Ground-Water Computer Models - State of the Art,"

Ground Water, Vol 17, No. 2, Mar-Apr 1979, pp 167-173. Available from:

Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

241. Prickett, T. A., "Modeling Techniques for Groundwater Evaluation,"

Advances in Hydroscience, Vol 10, 1975, V. T. Chow, ed., Academic Press,

New York. Available from: Technical Information Center, U. S. Army

Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg,

MS 39180-0631.

242. Prickett, T. A., and Lonnquist, C. G., "Selected Digital Computer

Techniques for Groundwater Resource Evaluation," Bulletin 55, 1971,

Illinois State Water Survey, Urbana, Ill. Available from: Technical

A-23
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30 Sep 86

243.

244.

245.

246.

247.

248.

249.

250.

251.

Information Center, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

Quirk, J. P., and Schofield, R. J., "The Effect of Electrolyte

Concentration on Soil Permeability," Journal of Soil Science, Vol 6,

No. 2, 1955, pp 163-178. Available from: Technical Information Center,

U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

Radukic, V., "Observed Behavior of Embankment Dams at Some Typical

Interfaces," Proceedings, Thirteenth International Congress on Large

Dams, India, Vol 1, 1979, pp 1005-1922. Available from: Technical

Information Center, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

Rouse, H., and Ince, S., History of Hydraulics, State University of

Iowa, Iowa City, 1957. Available from: Technical Information Center,

U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

Royster, D. L. "Some Observations on the Use of Horizontal Drains in

the Correction and Prevention of Landslides," Tennessee Department of

Transportation, Nashville, Tenn. 1977. Available from: Technical

Information Center, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

Rushton, K. R., and Redshaw, S. C., Seepage and Groundwater Flow, Wiley,

New York, 1979. Available from: Technical Information Center, U. S.

Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg,

MS 39180-0631.

Ryan, C. R., "Slurry Cut-Off Walls, Design and Construction," paper

presented at Slurry Wall Construction, Design, Techniques, and

Procedures Course, Chicago, Ill., Apr 1976. Available from: GO-CON,

Inc., P. O. Box 17380, Pittsburgh, PA 15235.

Ryan, C. R., "Slurry Cut-Off Walls, Design Parameters and Final

Properties," paper presented at Slurry Wall Construction, Design,

Techniques, and Procedures Course, Miami, Fla., Feb 1977. Available

from: GO-CON, Inc., P. O. Box 17380, Pittsburgh, PA 15235.

Schwartz, P. H., Analysis and Performance of Hydraulic Sand-Fill Levees,

Ph. D Thesis, University of Iowa City, Iowa, May 1976. Available from:

Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Scott, R. F., Principles of Soil Mechanics, Addison-Wesley, Reading,

Mass., 1963. Available from: Technical Information Center, U. S. Army

Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg,

MS 39180-0631.

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252. Sherard, J. L., A Study of the Influence of the Earthquake Hazard on the

Design of Embankment Dams, Jul 1966, Woodward, Clyde, Sherard & Associates, Oakland, Calif. Available from: Technical Information Center,

U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

253. Sherard, J. L., "Earthquake Considerations in Earth Dam Design," Journal

of the Geotechnical Engineering Division, Vol 93, No. SM4, Jul 1967,

American Society of Civil Engineers, New York. Available from: Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

254. Sherard, J. L., "Sinkholes in Dams of Coarse, Broadly Graded Soils,"

Transactions of the 13th International Congress on Large Dams, New

Delhi, India, Vol 11, 1979, pp 25-35. Available from: Technical

Information Center, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

255. Sherard, J. L., "Some Considerations Concerning Underseepage Control for

Earth Dams," Proceedings of the Symposium on Earth and Rockfill Dams,

India, Vol 1, 1968, pp 204-214. Available from: Technical Information

Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

256. Sherard, J. L., et al., Earth and Earth-Rock Dams, Wiley, New York,

1963. Available from: Technical Information Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg,

MS 39180-0631.

257. Singh, B., and Sharma, H. D., Earth and Rockfill Dams, Sarita Prakashan,

India, 1976. Available from: Technical Information Center, U. S. Army

Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg,

MS 39180-0631.

258. Snow, D. T., A Parallel Plate Model of Fractured Permeability Media,

Ph. D Dissertation, 1965, University of California, Berkeley, Calif.

Available from: Technical Information Center, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

259. Soletanche, "Laguna Dam, Mexico, 1970," Paris, France. Available from:

RECOSOL, Rosslyn Center, 1700 North Moore Street, Suite 2200, Arlington,

VA 22209.

260. Soletanche, "Los Reyes Dam, Mexico, 1972," Paris, France. Available

from: RECOSOL, Rosslyn Center, 1700 North Moore Street, Suite 2200,

Arlington, VA 22209.

261. Soletanche, "Nexapa Dam, Mexico, 1971-1972," Paris, France. Available

from: RECOSOL, Rosslyn Center, 1700 North Moore Street, Suite 2200,

Arlington, VA 22209.

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262.

263.

264.

265.

266.

267.

268.

269.

270.

271.

Soletanche, "Tenango Dam, Mexico, 1971," Paris, France. Available from:

RECOSOL, Rosslyn Center, 1700 North Moore Street, Suite 2200, Arlington,

VA 22209.

Soletanche, "The Razaza Dam, Iraq, 1969," Paris, France. Available from:

RECOSOL, Rosslyn Center, 1700 North Moore Street, Suite 2200, Arlington,

VA 22209.

Sowers, G.

House, New

U. S. Army

Vicksburg,

F., Earth and Rockfill Dam Engineering, Asia Publishing

York, 1962. Available from: Technical Information Center,

Engineer Waterways Experiment Station, P. O. Box 631,

MS 39180-0631.

Sowers, G. F., "Earth Dam Failures," Lectures of the Seminar, Failures

of Large Dams, Reasons and Remedial Measures, W. Wittke, ed., Publication No. 4, 1977, Institute for Foundation Engineering, Soil Mechanics,

Rock Mechanics, and Waterways Construction, Aachen, Germany, pp 178-226.

Available from: Technical Information Center, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Stephenson, D., Rockfill Hydraulic Engineering, Elsevier, New York,

1979. Available from: Technical Information-Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg,

MS 39180-0631.

Strohm, W. E., Nettles, E. H., and Calhoun, C. C., "Study of Drainage

Characteristics of Base Course Materials," Symposium on Subsurface

Drainage, Highway Research Record 203, 1967, pp 8-28, Highway Research

Board. Washington. D. C. Available from: Technical Information Center,

U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

Taylor, D. W., Fundamentals of Soil Mechanics, Wiley, New York, 1948.

Available from: Technical Information Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Taylor, H., and Chow, Y. M., "Design Monitoring, and Maintaining

Drainage System of a High Earthfill Dam," Transactions, Twelfth

International Congress on Large Dams, Mexico, Vol 2, 1976, pp 147-167.

Available from: Technical Information Center, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

Telford, W. F., et al., Applied Geophysics, Cambridge University Press,

New York, 1976. Available from: Technical Information Center, U. S.

Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg,

MS 39180-0631.

Telling, R. M., Menzies, B. K., and Coulthard, J. M., "A Design Method

for Assessing the Effectiveness of Partially Penetrating Cut-Off Walls,"

Ground Engineering, Vol 11, No. 8, Nov 1978, pp 48-51. Available from:

Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

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272. Telling, R. M., Menzies, B. K., and Simons, N. E., "Cut-Off Efficiency,

Performance and Design," Ground Engineering, Vol 11, No. 1, Jan 1978a,

pp 30-43. Available from: Technical Information Center, U. S. Army

Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg,

MS 39180-0631.

273. Telling, R. M., Menzies, B. K., and Simons, N. E., "The Effectiveness of

Jointed Cut-Off Walls Beneath Dams on Pervious Soil Foundations," Ground

Engineering, Vol 11, No. 4, May 1978b, pp 27-37. Available from:

Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

274. Terzaghi, K., Theoretical Soil Mechanics, Wiley, New York, 1943. Available from: Technical Information Center, U. S. Army Engineer Waterways

Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

275. Terzaghi, K., and Peck, R. B., Soil Mechanics in Engineering Practice,

2d ed., Wiley, New York, 1967. Available from: Technical Information

Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

276. Theis, C. V. "The Relation Between the Lowering of the Piezometric

Surface and the Rate and Duration of Discharge of a Well Using

Groundwater Storage," Transactions of American Geophysics Union, Vol 16,

1935, pp 519-524. Available from: Technical Information Center, U. S.

Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg,

MS 39180-0631.

277. Thomas, H. H., The Engineering of Large Dams, Vol II, Wiley, 1976.

Available from: Technical Information Center, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

278; Todd, D. D., and Bear, J., "River Seepage Investigation," Water Resources

Center Contribution No. 20, Sep 1959, Hydraulic Laboratory, University of

California, Berkeley. Available from: Technical Information Center,

U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

279. Todd, D. K., Groundwater Hydrology, 2nd ed., Wiley, New York, 1980.

Available from: Technical Information Center, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

280. Turkish National Committee, "Investigation of Leakages at Keban Dam,"

Transactions of the Twelfth International Congress on Large Dams, Vol II,

1976, Mexico City, pp 459-483. Available from: Technical Information

Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

281. Twelker, N. H., "Analysis of Seepage in Pervious Abutments of Dams,"

Proceedings of the Fourth International Conference on Soil Mechanics and

Foundation Engineering, London, England, Vol 2, 1957, pp 389-393.

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Available from: Technical Information Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

282. Vaughan, P. R., "Design of Filters for the Protection of Cracked Dam

Cores Against Internal Erosion," Preprint 3420, Oct 1978, American

Society of Civil Engineers, New York. Available from: Technical Information Center, U. S. Army Engineer Waterways Experiment Station, P. O.

Box 631, Vicksburg, MS 39180-0631.

283. Vaughan, P. R., et al., "Cracking and Erosion of the Rolled Clay Core of

Balderhead Dam and the Remedial Works Adopted for Its Repair," Transactions of the Tenth International Congress on Large Dams, Vol 1, 1970,

Montreal, Canada, pp 73-93. Available from: Technical Information

Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

284. Veder, C., "Closing Address," Diaphragm Walls and Anchorages, 1975,

pp 221-225, Institution of Civil Engineers, London. Available from:

Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

285. Veder, C., "Excavation of Trenches in the Presence of Bentonite

Suspension for the Construction of Impermeable and Load-Bearing

Diaphragms," Grouts and Drilling Muds in Engineering Practice,

Butterworths, London, 1963, pp 181-188. Available from: Technical

Information Center, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

286. Vennard, J. K., Elementary Fluid Mechanics, 4th ed., Wiley, New York,

1965. Available from: Technical Information Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg,

MS 39180-0631.

287. Walton, W. C., "Selected Analytical Methods for Well and Aquifer Evaluation," Bulletin 49, 1962, Illinois State Water Survey, Urbana, Ill.

Available from: Technical Information Center, U. S. Army Engineer

Waterways Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

288. Wei, C.-Y., and Shieh, W. Y. J., "Transient Seepage Analysis of Guri

Dam," Journal, Technical Councils, American Society of Civil Engineers,

Vol 105, No. TCl, Apr 1979, pp 135-147. Available from: Technical

Information Center, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

289. Wilkins, J. K., "Flow of Water Through Rockfill and Its Application to

the Design of Dams," Proceedings, Second Australia-New Zealand

Conference on Soil Mechanics and Foundation Engineering, New Zealand,

1956, pp 141-149. Available from: Technical Information Center, U. S.

Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg,

MS 39180-0631.

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290. Wilson, C. R., and Witherspoon, P. A., "An Investigation of Laminar Flow

in Fractured Porous Rocks," 1970, Department of Civil Engineering,

University of California, Berkeley, Calif. Available from: Technical

Information Center, U. S. Army Engineer Waterways Experiment Station,

P. O. Box 631, Vicksburg, MS 39180-0631.

291. Wilson, S. D., and Marsal, R. J., "Current Trends in Design and Construction of Embankment Dams," 1979, American Society of Civil Engineers. Available from: Technical Information Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631, Vicksburg,

MS 39180-0631.

292. Winter, G., and Nilson, A. H., Design of Concrete Structures, 9th ed.,

McGraw-Hill, New York, 1979. Available from: Technical Information

Center, U. S. Army Engineer Waterways Experiment Station, P. O. Box 631,

Vicksburg, MS 39180-0631.

293. Xanthakos, P. P., Slurry Walls, McGraw-Hill, New York, 1979. Available

from: Technical Information Center, U. S. Army Engineer Waterways

Experiment Station, P. O. Box 631, Vicksburg, MS 39180-0631.

294. Yong, R. N., and Warkentin, B. P., Introduction to Soil Behavior,

Macmillan, New York, 1966. Available from: Technical Information

Center, U. S. Army Engineer Waterways Experiment Station, P. O.. Box 631,

Vicksburg, MS 39180-0631.

295. Younger, J. S., and Lim, C. I., "An Investigation into the Flow Behavior

Through Compacted Saturated Fine-Grained Soils with Regard to Fines

Content and over a Range of Applied Hydraulic Gradients," Fundamentals

of Transport Phenomena in Porous Media, International Association for

Hydraulic Research, New York, 1972, pp 312-326. Available from:

Technical Information Center, U. S. Army Engineer Waterways Experiment

Station, P. O. Box 631, Vicksburg, MS 39180-0631.

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APPENDIX B

APPROXIMATE METHODS FOR ANALYSIS OF FLOW PROBLEMS

B-1. Introduction. As previously mentioned in Chapter 4, various methods are

available, in addition to flow nets, for solving idealization of seepage problems. As shown in figure 4-3, these methods include electrical analogy,

hydraulic or sand tank models, viscous flow models, method of fragments, finite

difference method, and finite element method. Prior to conducting an analysis,

the problem to be studied must be defined in terms of:

a. Aquifer and embankment dimensions.

b. Coefficients of permeability of the embankment and foundation soils.

c. Horizontal to vertical permeability ratios.

d. Boundary conditions (impermeable and symmetrical).

e. Exits and entrances (fixed potential areas).

f. Head versus time relationships for unsteady flow.

Sensitivity studies may be run to establish the effect of parameters not known

accurately.

B-2. Electrical Analogy.

a. General. Processes which involve movement of current due to differences in energy potential operate on the same principles as movement of confined ground water as shown in table B-l. Therefore, to obtain the pattern of

equipotential lines or flow lines (see figure 4-4), the flow domain is transferred by an electrical conductor of similar geometric form as first proposed

by Pavlovsky in 1918 (Harr 1962). Electrical analogies may involve twodimensional conducting paper models or three-dimensional tanks containing

aqueous solution.

b. Two-Dimensional Models. When field conditions can be approximated

by a two-dimensional plan or section, teledeltos conducting paper models may

be used to obtain a flow net. Two-dimensional teledeltos models are simple to

use and can accommodate various geometries. However, it is difficult to simulate varying permeabilities and they are generally restricted to steady state

confined aquifers (Bear 1972, Boer and Molen 1972).

c. Three-Dimensional Models. The use of electrical analogy models is

described by various authors (Zangar 1953, Todd and Bear 1959, and Duncan

1963). The three-dimensional electrical analogy model at the U. S. Army

Engineer Waterways Experiment Station (WES) (see figure B-l) is a plexiglass

tank filled with dilute copper sulfate solution and having a calibrated

elevated carrier assembly for the accurate placement of a point electrode probe

B-1
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Table B-1. Analogy Between Darcy's Law and Ohm's Law (a)

Darcy's Law Ohm's Law

Q = rate of flow or water I = current (rate of flow of electricity)

K = coefficient of permeability K' = conductivity coefficient

A = cross-sectional area A ' = cross-sectional area

H = head producing flow V = voltage producing current

L = length of path of percolation L' = length of path of current

(a) From Bureau of Reclamation. 127

anywhere in the fluid. Extensive use of the WES model has been made to:

(1) Determine uplift values and seepage quantities for use in the

design of Columbia Lock and Dam, Louisiana (Duncan 1962).

(2) Determine the uplift values and seepage quantities for fully and

partially penetrating well arrays from line and circular sources (Duncan 1963,

Banks 1963, and Banks 1965).

(3) Determine uplift pressures beneath the spillway, piezometric heads

at the downstream toe of the dam, and total seepage quantities for use in the

design of Oakley Dam, Illinois (McAnear and Trahan 1972).

B-3. Sand Tank Model. The sand tank model (hydraulic model), as shown in

figure B-2, consists of a rigid, watertight container with a transparent front,

filled with sand, deaired water,(1) and measuring devices. The geometry of the

sand tank corresponds to that of the prototype. The sand may be placed under

water to provide a homogeneous condition, or layers of different sand sizes may

be used to study anisotropy. If the flow is unconfined and the same material

is used for model and prototype, the capillary rise must be compensated for in

the model. When a steady-state flow is reached, dye can be introduced at

various points along the upstream boundary close to the front wall to form

traces of the streamlines. Piezometers are used to measure the pressure heads

at various locations (Bear 1972 and Harr 1962). A sand tank model was employed

to investigate the effect of length of horizontal drain on the through seepage

flow nets and quantities for a homogeneous and isotropic sand embankment

(1) For prolonged tests, disinfectants such as Formol should be added to the

water to prevent bacterial growth that causes clogging (Bear 1972).

B-2
B-3

Figure B-1. Three-dimensional electrical analogy apparatus (after Duncan3
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PARTIALLY PENETRATING WELL

WITH A CIRCULAR SOURCE

SEEPAGE FROM CANALS

TRACER DYE

SEEPAGE IN EMBANKMENTS

Figure B-2. Hydraulic or sand tank model

(prepared by WES)

B-4
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(Brand and Armstrong 1968). Sand tank models are also used extensively in

petroleum engineering, ground-water quality, and pollution research (Bear 1972

and Prickett 1979).

B-4. Viscous Flow Models. The viscous flow model, also called the Hele-Shaw

or parallel plate model, is based on the similarity between the differential

equations governing saturated flow in a porous medium and those describing the

flow of a viscous liquid in the narrow space between two parallel plates. The

viscous flow model contains the shape of the structure to be Investigated and

once a steady-state flow is obtained, colored dyes can be injected along the

upstream edge and patterns of streamlines can be observed. A camera (movie or

still) is normally used to record the results of experiments. Inhomogeneous

hydraulic conductivity, such as would exist in a zoned earth dam, can be simulated by varying the width of the interspace between the parallel plates, as

shown in figure B-3. The viscous flow model experiments should be conducted in

a temperature-controlled room because viscosity plays an important role in

analog scaling. If this is not feasible, the temperature should be measured at

all inflow and outflow points during the test and scales must be recomputed

according to the varying average temperature of the liquid in the model (Bear

1972 and Harr 1962). A viscous flow model was constructed at WES to simulate

seepage conditions induced in streambanks by sudden drawdown of the river level.

The results from the model study compared favorably with field observations,

finite difference, and finite element methods (Desai 1970 and Desai 1973).

B-5. Method of Fragments.

a. General. The method of fragments is an approximate analytical

method for the computation of flows and pressure heads for any ground-water

system. The underlying assumption of this procedure developed by Pavlovsky in

1935 (Pavlovsky 1956 and Harr 1962) is that equipotential lines at various

critical locations in the flow region can be approximated by straight vertical

lines. These equipotential lines divide the flow region into parts or fragments. Other assumptions inherent in the method of fragments procedure are

(a) Darcy's law is valid, (b) steady-state flow exists, and (c) the soil medium

is approximated as a single homogeneous and isotropic layer or at series of

such layers. The transformation of anisotropic soil to an equivalent isotropic

soil is described in Section 4.7 of this manual.

b. Basic Concepts. The quantity of flow through a single fragment is

computed as:

(B-1)

where

k - coefficient of permeability

hi = head loss through the fragment

= dimensionless form factor, = Ne/Nf

B-5
EM 1110-2-1901

30 Sep 86

a. Homogeneous earth dam

b. Zoned earth dam

Figure B-3. Viscous flow model (courtesy of Bear 140)

B-6
EM 1110-2-1901

30 Sep 86

Because the fragment boundaries consist of equipotential lines, the flow

through each fragment must be equal to the total flow through the system. Thus

Since summation of the head loss in each fragment is

loss, the total quantity of flow can be expressed as

where h is the total head loss through the section

head loss in each fragment can be calculated from

. Along the same line, the

(B-2)

equal to the total head

(B-3)

(B-4)

The head loss along any impermeable boundary of a fragment is assumed to

change linearly. Thus the head loss within fragment i up to point A is

equal to the head loss in the fragment times the ratio of the length of the

boundary to point A to the total length of boundary. The basic concept of the

method of fragment procedure is to break the flow region into parts for which

the form factor is shown in figure B-4 (Harr 1977). This manual will describe

how to calculate the factors for each type of fragment (Harr 1962 and Harr

1977).

c. Fragment Types. There are currently nine different fragment types.

Of these, the first six are for confined flow while the last three are for

unconfined flow.

(1) Type I. This fragment type represents a region of parallel

horizontal flow between impervious boundaries. For this internal type

fragment, shown in figure B-5a, the flow per unit width is equal to

(B-5)

B-7
EM 1110-2-1901

30 Sep 86

Thus from Equation B-l, the form factor is

An elemental Type I section shown in figure B-5b illustrates that

(B-6)

(B-7)

This elemental section will be used to derive the form factors for fragment

types IV, V, and VI.

(2) Type II. This fragment type represents a vertical impervious

boundary embedded a length S into a pervious layer of thickness T . This

fragment can represent either an entrance condition (figure B-6a) or an exit

condition (figure B-6b). The form factor is obtained from the plot in

figure B-4 where the scale of is given as one-half the reciprocal of

Q/kh or

(B-8)

The form factor could also be expressed as the ratio of the elliptic integral

of the first kind with modulus m over the elliptic integral of the complementary modulus, m' . For this fragment type, the modulus value is a function of

the ratio S/T . The graph in figure. B-7 was obtained by solving the elliptic

integrals for various combinations of S/T . For the type II fragments, the

ratio of b/T equals 0 .

(3) Type III. This type of fragment represents an impervious layer of

length b , a vertical boundary of depth S , in a pervious layer of thickness

T . Either of the sections shown in figure B-8 can represent this fragment

type. The form factor is obtained directly from figure B-7 with b/T other

than zero. For this case, the elliptic integral modulus is a function of both

b/T and S/T .

(4) Type IV. This type is an internal fragment with boundary length

b , embedment length S , in a pervious layer of thickness T . Figure B-9a

illustrates the two possible configurations. Pavlovsky divided the flow region

into active and passive parts based on the results of electrical analogue tests

as shown in figure B-9b by line AB . An angle of 45 deg was assumed for the

line dividing the two parts of the fragment. This resulted in two cases,

depending on the relation between b and S . For the case where b < S , the

B-8
B-9

Fragmcnl 

1rpc 

II 

Ill 

IV 

Illustration Form f<Klor, 11• t h is head lns'i 

ct• ... ,_ 

II 

t<th),Fig.5-13 

= I Fig. 5-13 

b::ss: b 

«<•=ln(l+;;-) 

+ b- - ---' 

T 

Fragment 

--

v 

VI 

VII 

VIII 

IX 

llluslruliun 

y 

Form fm.:lor. 11t ( 

luss fnt

- -

-- 

L s 2s: 

= 2 In (I + 

L2!2s: 

(I+ 

L 2: s' + s": 

= In I (I + 

I. - ( s' + s"l +-------

T 

L ::s s' + s": 

= In I (I 

where L

,'1' =-

h" =!_,=

Figure B-4. Summary of fragment types and form factors (courtesy of McGraw

181 Book Company ) 
EM 1110-2-1901

30 Sep 86

Figure B-5. Type I fragment (courtesy of McGraw-Hill

Book Company 181 )

Figure B-6. Type II fragment (courtesy of McGraw-Hill

Book Company 181 )

B-10
EM 1110-2-1901

30 Sep 86

Figure B-7. Quantity of discharge for symmetrically

placed pilings (courtesy of McGraw-Hill Book

181

Company )

B-11

1.5 

1.4 

1.3 

1.2 

1.1 

1.0 

0.9 

-1~ 0.8 

II 0.7 ol~ 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

l 

j 

\ I u 

=-------_:~~ . " ~ \ I I i 

I ----- oo·a·· - - - - - 0 · .. Oo O;t:E"" - - - - - - P.O. .. wa· o - -

' I I I ,;;,,;gy:;..J§_2"fH··£C r\ I 

\ I I ~/,1'/ffiW/~$&##/m~r 

\t I 

r--... ~ ~~ I 

...... 

~~ I I 

I 

.-.!!so ~. I 

0. 7;-~~ I 

'- I 

l.OO-r---r---~ I 1.25 I ~ 

1.50 

I 

. . 

:,~ :::::::::::±-:: ~ ~ -...~ 

~ I 

........ ~: 

~ 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 

_s 

T 

(f 17"$ h2 TTb 2 TT S 

m = cos Ti tan 2 t + tan 2T 

Q 1 4 for m s 0.3, kh = -;r In m 

2 09...Q_ __ ,. for m ~ . . kh - 1 2 

21n(--...':!!.) 16 
EM 1110-2-1901

30 Sep 86

(a) (b)

Figure B-8. Type III fragment (courtesy of McGraw-Hill

Book Company 181 )

active zone is composed of elements of type I fragments of width dx illustrated in figure B-9c. The form factor is the integral of dx over y from

0 to b which results in a form factor of

(B-9)

If b > S, then the fragment can be divided into two fragments as shown in

figure B-9e. The first is a type IV with b > S and the second is a type I

fragment with L equal to b - S . Thus the form factor is the sum of the

form factors which would be

(B-10)

(5) Type V. This fragment type has two vertical boundaries of equal

embedment S in a pervious layer of thickness T . As shown in figure B-10,

the form factor for this fragment is twice that for the type IV fragment.

B-12
EM 1110-2-1901

30 Sep 86

Figure B-9. Type IV fragment (courtesy of McGraw-Hill Book

181

Company )

B-13
EM 1110-2-1901

30 Sep 86

Figure B-10. Type V fragment (courtesy of McGraw-Hill

Book Company 181)

Since there were two cases of type IV fragment, there are two cases for the

type V fragment. The two cases are for L < 2s and L > 2S . For the first

case, the form factor is

(B-11)

For the second case which consists of a type I fragment within two type IV

fragments, the form factor is

(B-12)

(6) Type VI. This fragment type, illustrated in figure B-11, is the

same as the type V fragment except that the embedment lengths are different.

Using the same approximations as in fragment type IV, there are two cases for

the form factor. For the first case where L > (S' + S"), the form factor is

(B-13)

B-14
EM 1110-2-1901

30 Sep 86

Figure B-11. Type VI fragment (courtesy of McGraw-Hill

Book Company 181)

For the second case where L < (S' + S"), the form factor is

(B-14)

where

(7) Type VII. This fragment represents the condition of unconfined

flow. This flow is characterized by having one boundary of the flow domain as

a free surface (line AB in figure B-12). This free surface separates the

saturated region from that region where no flow occurs. From Darcy's law and

Dupuit's assumptions, the hydraulic gradient is (h1 - h2)/L and the

cross-sectional area is (h1 + h2)/2 , thus the flow is

(B-15)

B-15
EM 1110-2-1901

30 Sep 86

Figure B-12. Type VII fragment (courtesy of McGraw-Hill

Book Company 181 )

From this, the form factor is

(B-16)

(8) Type VIII. This fragment type represents an upstream slope

entrance condition on an earth dam of height hd and is illustrated in

figure B-13. It was assumed that the curve streamlines (cd) could be

approximated by horizontal flow channels of length ed (Pavlovsky 1956 and

Harr 1977). With this assumption, the hydraulic gradient in each channel is

(B-17)

B-16
EM 1110-2-1901

30 Sep 86

Figure B-13. Type VIII fragment (courtesy of McGraw-Hill

Book Company 181)

Integrating the ratio dy/(hd - y) from

for the quantity of flow as

0 to h generates the expression

(B-18)

(9) Type IX. This fragment type, shown in figure B-14, represents the

exit condition where the surface of seepage exists.

(DE) is not an equipotential line or a streamline.

The surface of seepage

Pavlovsky assumed that the

flow is horizontal. For the portion of the slope between D and E , the

flow is the coefficient of permeability times the integral of dy over

cot The flow for

a2dy over the cot

E to F is the permeability times the integral of

expression for the flow is

(a2 + h2 - y) . When the integration is performed, the

(B-19)

B-17
EM 1110-2-1901

30 Sep 86

Figure B-14. Type IX fragment (courtesy of McGraw-Hill

Book Company 181 )

d. Exit Gradient. The method of fragments procedure can be used to

determine the exit gradient discussed in paragraph 4.9 of this manual. For

this procedure, the last fragment (downstream) needs to be either a type II or

a type III fragment. The exit gradient is defined as (Harr 1962)

(B-20)

where

h

m

= head loss in the last fragment

K = complete elliptic integral of the first kind with modulus m

T = depth of flow region

As defined before, the modulus m is a function of both b/T and S/T and

is defined as

(B-21)

B-18
EM 1110-2-1901

30 Sep 86

Instead of calculating the various values, for type II fragments figure B-15

can be used with S/T to obtain the fraction for IES/hm . By substituting

the appropriate values, the exit gradient is calculated.

e. Example 1. The method of fragment procedure for confined flow will

be illustrated in the following example obtained for John H. Overton Lock and

Dam (U. S. Army Engineer District, St. Louis 1978). This problem will analyze

the steady state flow conditions for a two-dimensional idealization of the

lock structure. The quantity of flow and head along the bottom of the lock

will be determined. For illustrative purposes, the exit gradient procedure

will be included. The dimensions of the structure, shown in figure B-16, are

those used in the analysis after the cross section has been transformed to

account for soil anisotropy. The original analysis contained two soil layers,

but for illustrative purposes the soil will be modeled as one layer. The first

step is to determine the form factors for each region. The first region is a

type II fragment with S = 19 ft and T = 89 ft . Using figure B-7 with

S/T = 0.21 , the fraction for Q/kh = 0.78 , thus = 0.641 . Region 2 is a

type I fragment with L = 456 ft and a = 70 ft . From figure B-4, the form

factor for the type I fragment is equal to L/a , thus = 6.514 . The third

region is a type II fragment with S = 9 ft and T = 79 ft . Using figure B-7

with S/T = 0.114 , the fraction for Q/kh = 1.01 , thus = 0.495 . The

summation of the form factors is 7.650. The quantity of flow is calculated

from equation B-3. Using transformed permeability of 400 x 10-4 cm/sec and a

total head of 18 ft, the quantity of flow is calculated to be 266.8 ft3/day/

foot of lock width. The head loss in each fragment is calculated from equation B-4. The following table lists the head loss for each fragment in this

problem:

Region hi

1 0.641 1.51

2 6.514 15.33

3 0.495 1.16

= 7.650 = 18.00

The head along the bottom decreases from 16.49 ft at the upstream end to 1.16

at the downstream end. Using the assumption of a linear distribution of the

head loss within a fragment, the head at any point along the bottom of the

lock could be calculated as

head at pt a = 16.49 ft - distance to pt A for upstream of lock

total length of lock 15.33 ft (B-22)

B-19
EM 1110-2-1901

30 Sep 86

Figure B-15. Relationship for determining the exit gradient as a function

of the head loss in the fragment and geometry for a Type II fragment

(courtesy of McGraw-Hill Book Company

181

)

B-20
EM 1110-2-1901

30 Sep 86

Figure B-16. Transformed section of John H. Overton Lock simplified to one

soil layer (from U. S. Army Engineer District, St. Louis 112)

The exit gradient is calculated for region 3 which is a type II fragment.

Using S/T = 0.114 with figure B-15, the fraction for IES/hm is found to be

0.63. With a head loss of 1.16 ft in this fragment, the exit gradient is

calculated to be 0.082.

f. Example 2. This example will illustrate the method of fragment procedure for unconfined flow problems. The example is obtained from John H.

Overton Lock and Dam (U. S. Army Engineer District, St. Louis 1978). The

problem is to locate the free surface in the closure dam and to determine the

quantity of flow through the dam under steady state conditions. The dimensions of the structure shown in figure B-17 are after the material has been

transformed to account for soil anisotropy. This sample problem assumes an

impervious boundary at the base of the dam. To account for some flow under

the dam, the impervious boundary could be lowered. By lowering the boundary

to the lowest possible point, bounds for the problem would be established.

There are three fragment types in this earthen embankment. Region 1 is a

B-21
EM 1110-2-1901

30 Sep 86

Figure B-17. Transformed section of John H. Overton closure dam (from

U. S. Army Engineer District, St. Louis 112

)

type VIII fragment while region 2 is a type VII fragment and region 3 is a

type IX fragment. To calculate the flow through region 1, equation B-18 is

used with h

i

= 32 ft; hd = 37 ft, and = 19.9 deg (cot = 2.76).

Substituting into the equation produces

For region 2, the quantity of flow is calculated from equation B-15.

Substituting into this equation produces

(B-23)

(B-24)

For region 3, equation B-19 defines the quantity of flow. By substituting

cot = 2 and H2 = 14 ft produces

(B-25)

B-22
EM 1110-2-1901

30 Sep 86

From the embankment geometry, L can be defined as

(B-26)

By substituting into equation B-26, there are four equations with four

unknowns, h , a2 , Q/k , and L . There are several methods to solve these

four equations (Harr 1977). For the case where h2 = 0 , a reduction of

two equations and two unknowns occurs. For this example, equation B-23 will

be combined with equation B-24 and equation B-26 will be substituted for L .

This produces

Also equation B-23 can be combined with equation B-25, producing

(B-27)

(B-28)

Equations B-27 and B-28 have reduced the equations and unknowns by two. Thus

with two equations and two unknowns, a trial and error graphical process can

be used. The results of this process are shown in figure B-18 and indicate

that h = 28.9 ft and a2 = 0.9 ft., Substituting into equations B-23 and B-25

generates a Q/k value of 1.71 which results in an estimated flow of

242.4 ft3/day/ft of dam. Knowing h and a2 , the location of the phreatic

surface can be estimated.

g. Flow in Layered Systems. One of the limitations of the method of

fragments is that the flow layer is assumed to be homogeneous and isotropic.

An approximate procedure to determine flow characteristics of a layered system

was proposed by Polubarinova-Kochina (1941). Harr (1977) extended this method

as follows. The coefficients of permeability for the two layers are related by

a dimensionless parameter by the expression

where

(B-29)

k1

= coefficient of permeability of the upper layer

k2 = coefficient of permeability of the lower layer

B-23
EM 1110-2-1901

30 Sep 86

h

a

2

28.8 -0.4

29.0 2.1

30.0 8.6

31.0 13.6

h a

2

29.9 0.6

27.8 1.2

25.6 1.7

Equation B-27

Equation B-28

Figure B-18. Graphical solution-of equations B-27 and B-28

(from U. S. Army Engineer District, St. Louis 112

)

B-24
EM 1110-2-1901

30 Sep 86

The ratio of permeabilities can vary from 0 to infinity. Over this range,

ranges from 0 to 1/2. The basis of this method is to determine the flow and

head losses for three certain special cases of and then interpolate

between these values. The three special cases are as follows:

(1) = 0 . For to be equal to 0, k2 must equal 0. Therefore

the problem is reduced to a one-layer problem with a flow region thickness

equal to the upper layer.

(2) = 1/4 . For to be equal to 1/4, k2 must equal k1 .

Therefore, the problem is reduced to a one-layer problem with a flow region

the thickness of the upper and lower layers.

(3) = 1/2 . For to be equal to 1/2, k2 must be infinite. This

case represents the infinite flow where there is no resistance to flow in the

lower layer. Since Q/k1h = the inverse of this ratio is equal to zero.

This procedure can be expanded to a three-layer system by the use of two

values. The first value would be for the top two layers, while the second

would be for the bottom two layers.

h. Example 3. This example will illustrate the method of fragment procedure for confined flow in a two-layer system. The example is obtained from

John H. Overton Lock and Dam (U. S. Army Engineer District, St. Louis 1978).

This problem will analyze the steady-state flow conditions for the dam and

stilling basin. The quantity of flow and head along the bottom of the structure will be determined. For illustrative purposes, the exit gradient procedure will be included. The effect of various parameters like the length of

sheetpile cutoff can be studied using this procedure. The dimensions of the

structure, shown in figure B-19, are those used in the analysis after the cross

section has been transformed to account for soil anisotropy. There are three

fragments for this problem and three cases to be evaluated. For the first

case, 0 , all the flow is assumed to occur in the clay layer. Region 1 is

a type II fragment with S = 25 ft and T = 35 ft. Using figure B-7 with

S/T = 0.71 , the fraction for Q/kh = 0.36 , thus = 1.38 . The second

region is a type V fragment with S = 13 ft, T = 23 ft, and L = 73.5 ft.

Since L > 25 , equation B-13 is used to calculate the form factor. For the

above values, the form factor is 3.73. Region 3 is a type II fragment where

S = 24 ft and T = 34 ft. The form factor, using figure B-7, is calculated to

be 1.36. Using equation B-1, the ratio Q/k1 is 2.78 and k1/Q is 0.36 .

For the second case, = 1/4 , the flow is assumed to be equal in both layers.

The form factors are recalculated using the same fragment types. The value of

Q/k1 is 6.50 which results in a k1/Q value of 0.15. For the last case,

= 1/2 , all flow is assumed to be in the lower sand layer. Only vertical

flow occurs in the top or clay layer. For this case, Q/k1 is infinite which

results in a k1/Q of 0 . A plot of k1/Q versus is shown in figure B-20a. For this problem k2 is 200 times k1 , therefore equals 0.48.

B-25
EM 1110-2-1901

30 Sep 86

Figure B-19. Transformed section of John B. Overton Dam and stilling

basin for one case of sheet pile lengths (from U. S. Army Engineer

District, St. Louis 112)

By interpolation for = 0.48 , k1/Q equals 0.01 which results in a flow Q

of 56.7 ft3/day/ft of dam. To determine the head along the bottom of the

structure, the head at points A and B in figure B-19 must be determined. Using

the procedure described in example 1, equation B-22, the following head loss

and total head values are calculated.

Point A Point B

Head Loss Total Head Head Loss Total Head

ft ft ft ft

0 5.2 52.8 12.8 45.2

1/4 6.2 51.9 12.0 46.0

For the case where = 1/2 , the head anywhere along the bottom of the structure is equal to half the total head loss, or for this case 9 ft. Thus the

total head on points A and B is equal to 49 ft. Figure B-20b is the plot of

the total head versus and shows, for an of 0.48, the total head at

point A is 49.4 ft while the total head at point B is 48.5 ft. The exit gradient for each case is calculated by the procedure described in example 1.

For the case of 0 , the fraction IES/hm is 0.55 which with S = 24 ft

B-26
EM 1110-2-1901

30 Sep 86

Figure B-20. value plots for John H. Overton Dam and stilling

basin (from U. S. Army Engineer District, St. Louis 112 )

B-27

04 

0.3 

0 

' ~-0.2 

0.1 

1- 51 

LL. 

ci' 50 

<( 

~ 

...J 49 

<( 

1-

~ 48 

47 

46 

45 

IAI 

€ 

18) 

E 

0.5 

€ 

I C) 

0.5 
EM 1110-2-1901

30 Sep 86

and hm

IE S/hm

= 3.8 ft produces IE =

is 0.615 which with S =

IE = 0.128 . For the case where

the distance is the thickness of

0.087 . For the = 1/4 case, the fraction

24 ft and hm = 5.0 ft produces

= 1/2 , the head loss is the total head and

the top layer. Using the equation

the exit gradient is 0.265. The exit gradient versus plot is shown in

figure B-20c. For an value of 0.48, the exit gradient is 0.245.

(B-30)

i. Uses and Limitations. The method of fragment procedure should be

used as a design tool where various factors are changed to evaluate their

effect or as an analytical tool when quick approximate results are needed.

When numerous factors are varied, the construction of flow nets becomes very

tedious and time consuming. The method of fragment procedure will generate

reasonable results for problems where the assumptions are not greatly violated.

There are several points the user needs to be aware of when using this procedure. The flow region must be generalized so that it consists of horizontal

and vertical boundaries. The procedure models the actual flow paths within

the flow region, thus if there is any doubt as to the direction, a rough flow

net should be drawn. This becomes important when a small portion of a structure is modeled with several fragments because the flow could be modeled in

unnatural paths. The accuracy of the results is dependent upon how well the

fragment boundary actually represents vertical equipotential lines. The

greater the deviation, the greater the degree of error. However, for many

practical problems reasonable results are generated. Comparison of the method

of fragment results with finite element solutions for a one-layer system

showed that the quantity of flow values for the fragment procedure are within

8 percent of the finite element results, while the uplift values are within

38 percent of the finite element results. The Computer-Aided Structural Engineering (CASE) project has developed a computer program for the method of

fragments procedure with a user manual describing the program (Pace et al.

1984).

B-6. Finite Difference Method.

a. Method of Solution. As previously mentioned in Chapter 4, the

finite difference method solves the Laplace equations by approximating them

with a set of linear algebraic expressions. The approximation is mathematical

rather than physical. The early methods of solving finite difference expressions for Laplace's equation were based upon hand calculations by the relaxation method(1)

. However, more recently a wide range of finite difference

solutions suited to the digital computer have been developed. A description of

(1) For example, see Appendix A of EM 1110-2-2501.

B-28
EM 1110-2-1901

30 Sep 86

available methods used to solve finite difference problems including example

applications, case studies, and computer program listings is available (Rushton

and Redshaw 1979).

b. Advantages. Use of iterative techniques such as successive overrelaxation which converge to the correct solution allows solution of unconfined and transient flow problems, For simple problems, the finite difference

method is usually more economical than the finite element method (Rushton and

Redshaw 1979).

c. Disadvantages. The finite difference method is not suited to complex geometry, including sloping layers and pockets of materials of varying

permeability. Irregular grids are difficult to input. Therefore, zones where

seepage gradients or velocities are high cannot be accurately modeled (Rushton

and Redshaw 1979).

d. Applications. The finite difference method was used at WES to simulate seepage conditions in streambanks induced by sudden drawdown of the river

level. As mentioned previously, this study included a viscous flow model,

field observations, and application of the finite element and finite difference methods. The results of the study indicated that the finite difference

method provided satisfactory and economical solutions for transient unconfined

fluid flow in porous, anisotropic, and nonhomogeneous media (Desai 1970 and

Desai 1973). The finite difference method was used to predict the location of

the phreatic surface within a zoned embankment with arbitrary fluctuations of

the reservoir (Dvinoff 1970). Generalized digital computer programs have been

developed which use the finite difference method to simulate one-, two-, and

three-dimensional nonsteady flow problems in heterogeneous aquifers under

water table and artesian conditions (Prickett and Lonnquist 1971 and Desai

1977). The finite difference method has been used to predict unsteady flow in

gravity wells. Good agreement was found between computed results and

laboratory test results obtained using a sand tank model (Desai 1977).

B-7. Finite Element Method.

a. Method of Solution. As previously mentioned in Chapter 4, the

finite element method is conceptually a physical rather than a mathematical

approximation. The flow region is subdivided into a number of elements and

permeabilities are specified for each element. Boundary conditions are specified in terms of heads and flow rates and a system of equations is solved to

compute gradients and velocities in each element (Desai and Abel 1972 and Desai

1977). Two- and three-dimensional finite element seepage computer programs for

both confined and unconfined flow problems have been developed at WES. Steadystate and transient problems (that can be treated as a series of steady-state

problems) can be solved (Tracy 1973a; Tracy 1973b; and Hall, Tracy, and

Radhakrishnan 1975). An interactive graphics preprocessor is available to

generate the finite element grid (Tracy 1977a). It is possible to compute the

stream function and potential and plot contours of these values to obtain the

flow net (Christian 1980 and Christian 1980). Details concerning the selection

of spatial and time meshes, computer time required, convergence, and stability

are available (Desai 1977). Also, an interactive graphics postprocessor is

available to assist in the analyses of the finite element results (Tracy

B-29
EM 1110-2-1901

31 Jul 86

1977b). A listing of finite element seepage computer programs used within the

Corps is available (Edris and Vanadit-Ellis 1982).

b. Advantages. The finite element method is well suited to complex

geometry, including sloping layers and pockets of materials of varying permeability. By varying the size of the elements, zones where seepage gradient or

velocity is high can be accurately modeled.

c. Disadvantages. The finite element method is usually more costly than

the finite difference method for simple problems (Rushton and Redshaw 1979).

d. Applications. The finite element method has been used in several

cases to provide solutions to seepage problems.

(1) WES studies. As discussed previously, the finite element method was

used at WES to simulate seepage conditions in streambanks induced by sudden

drawdown of the river level. This study included a viscous flow model, field

observations, and application of the finite difference and finite element

methods. The results of the study indicated that the finite element method

provided satisfactory solutions for transient unconfined fluid flow in porous,

anisotropic, and nonhomogeneous media (Desai 1970 and Desai 1973).

(2) Location of phreatic surface. The finite element method has been

used to determine the location of the phreatic surface in earth dams (Isaacs

1979; Isaacs 1980; Wei and Shieh 1979; and Desai and Kuppusamy 1980). The

finite element method was used to locate the phreatic surface within tailings

pond embankments and to define the subsurface flow of water from the pond.

Results predicted using the finite element model were confirmed with

measurements in a laboratory model and in the field (Kealy and Busch 1971).

(3) W.A.C. Bennett Dam. The finite element method was used to assess

the potential seepage flows and uplift pressures in the foundation rock for

W.A.C. Bennett Dam in British Columbia, Canada (see figure B-21). The finite

element analysis (see figure B-22) was carried out assuming the following

conditions:

(a) With an effective grout curtain.

(b) Without an effective grout curtain.

(c) With a drainage system.

(d) Without a drainage system.

(e) With various rock permeabilities.

The results of the finite element analysis, shown in figure B-23, indicate the

greatest reduction in seepage flow and hydrostatic pressure could be accomplished by an effective grout curtain and downstream-drainage system (Taylor

and Chow 1976).

B-30
EM 1110-2-1901

30 Sep 86

Figure B-21. Cross section of W.A.C. Bennett Dam, British Columbia,

Canada (courtesy of International Commission on Large Dams 269

)

(4) Corps of Engineers levees. The finite element method was used by

the U. S. Army Engineer District, Rock Island, to study hydraulic sand fill

levees along the Mississippi River (Schwartz 1976). Finite element and

gradient plane (1) analyses were used in conjunction with data from a full scale

test levee to establish the material properties of the sand levees and to

determine the exit point of the free seepage surface, the quantity of through

seepage, and the exit gradients along the free discharge face. A parameter

study was performed and dimensionless design charts were developed.

(5) Reservoir loading conditions on zoned embankments. The use of the

finite element method to study the effect of initial filling of the reservoir,

steady seepage, and rapid drawdown of the reservoir on zoned embankments has

been given (Eisenstein 1979).

(6) Bureau of Reclamation dams. The Bureau of Reclamation has utilized

two- and three-dimensional finite element methods, electrical. analogy, and

mathematical methods to analyze seepage flow through a dam embankment and

(1) The gradient plane method is a graphical solution by means of the hodograph (see description by Casagrande 1937).

B-31
EM 1110-2-1901

30 Sep 86

Figure B-22. Finite element study results (courtesy of International

Commission on Large Dams 269)

Figure B-23.

International

Uplift pressure under various

Commission on Large Dams269)

conditions (courtesy of

B-32
EM 111O-2-1901

30 Sep 86

foundation (Mantei and Harris 1979). Narrows Dam, Colorado, on the South

Platte River, was analyzed for seepage at the feasibility stage. Because of a

pervious foundation, the planners called for a positive vertical cutoff by

constructing a slurry wall down to the underlying shale. However, near the

right abutment the shale drops away to depths too great for economical slurry

wall construction. A three-dimensional finite element model (see figure B-24)

was used to determine the vertical exit gradients at the downstream toe of the

dam. The finite element method was used to study the effect of a toe drain,

partial depth slurry trench, partially and fully penetrating relief wells (see

figure B-25). Calamus Dam, Nebraska, on the Calamus River, was also analyzed

by the Bureau of Reclamation for seepage at the feasibility stage (Mantei and

Harris 1979; Mantei, Esmiol, and Cobb 1980; Mantei and Cobb 1981; and Cobb

1984). Calamus Dam has a setting very similar to Narrows Dam in the sense that

it is an earth dam on a pervious foundation. However, the underlying shale at

Calamus Dam is at such a great depth that it cannot be used as the base for a

cutoff wall as it was for Narrows Dam. Early thinking on the project involved

the use of a slurry trench cutoff down to a pervious sandstone fromation. A

three-dimensional finite element model (see figure B-26) was used to determine

the effects of an embankment toe drain, slurry trench under upstream blanket,

and/or relief wells at the downstream toe of the dam on the seepage rates and

hydraulic gradients in the dam foundation. Time and expense in operating the

large three-dimensional finite element models made it necessary that

be given to studying the various design alternatives using the best estimate

priority

of permeability for each foundation material rather than conducting sensitivity studies to establish the effect of varying the permeability (see paragraph B-l). The three-dimensional finite element models were five elements

deep, with the bottom layer of elements representing the sandstone, the next

layer sand and gravel, recent alluvium, interbedded fine sand, and dune sand.

A detailed three-dimensional finite element model was made for the outlet

works area that defined more of the design details, such as the filter blanket

under the stilling basin and channel and water table elevation controls, to

study the effectiveness of relief wells around the stilling basin.

(7) Corps of Engineer dams. The finite element method was used by the

U. S. Army Engineer District, Huntington,(1) in a reanalysis of the underseepage at Bolivar Dam, Ohio, completed in 1938 on Sandy Creek (U. S. Army Engineer

District, Huntington 1977a). A two-dimensional finite element model (see figure B-27) was used to determine the effects of an embankment toe drain, upstream impervious blanket, and proposed relief wells on seepage quantities,

exit gradients, and uplift pressures. A sensitivity study was conducted using

the two-dimensional finite element model to determine the influence of various

pool and rock surface levels, the permeability ratio of foundation soils, the

existence of a downstream gravel layer, and the effective source of seepage

entry upon underseepage. Typical test results for one set of boundary conditions and permeability values are given in figure B-28. Additional applications of the two-dimensional finite element method to conduct sensitivity

analysis to assess the effect of permeability anisotropy and various seepage

control measures was given by Lefebvre and coworkers (Lefebvre, Part, and

(1) Work was performed by Soil Testing Services, Inc., Northbrook, Illinois.

B-33
EM 1110-2-1901

30 Sep 86

Figure B-24. Contours of exit gradient from three-dimensional finite

element model study of Narrows Dam, Colorado (courtesy of American

Society of Civil Engineers 217

)

B-34

~xis of Dam 

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EM 1110-2-1901

30 Sep 86

Figure B-25. Vertical exit gradients from three-dimensional finite

element model study of Narrows Dam, Colorado (courtesy of American

Society of Civil Engineers 217 )

B-35

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D 3-0 MODEL WITHOUT REUEF WELLS 

0 2-o MODEL W\THOUT RELIEF WELLS 

~ QUASI 3-0 MODEL WtTH RELIEF WELLS 

AT 100' SPACING 
EM 1110-2-1901

30 Sep 86

Figure B-26. Grid for three-dimensional finite element model

study of Calamus Dam, Nebraska (courtesy of American Society

of Civil Engineers 217 )

B-36
B-37

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(from U. S. Army Engineer District, Huntington88) 
B-38

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88 Army Engineer District, Huntington ) 
EM 1110-2-1901

30 Sep 86

Tournier 1981). The finite element method was used by the U. S. Army Engineer

District, Huntington, (1) in a reanalysis of the underseepage at Mohawk Dam,

Ohio, completed in 1937 on the Walhonding River (U. S. Army Engineer District,

Huntington 1979b). A three-dimensional finite element model (see figure B-29)

was used to study the cause of unusually high relief well flows. Typical test

results for one set of boundary conditions are given in figure B-30.

(1) Work was performed by Soil Testing Services, Inc., Northbrook, Illinois.

B-39
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89 (from U. S. Army Engineer District, Huntington ) 
EM 1110-2-1901

30 Sep 86

APPENDIX C

ANALYSIS OF PRESSURE INJECTION TESTS (Ziegler 1976)

C-1. Water Pressure Tests

a. Water pressure tests are conducted by pumping water into a borehole

at a constant pressure and measuring the flow rate. Water enters the rock mass

along the entire length of borehole or along a test section (i.e., borehole

interval) sealed off by one or more packers as shown in figure C-1. The test

is rapid and simple to conduct and by conducting tests within intervals along

the entire length of borehole, a permeability profile can be obtained.

b. In most pressure tests the water injection pressure is limited to a

value which is not expected to produce an increase in the fracture width. An

increase in the fracture width will cause erroneously high flow rates resulting in higher permeabilities than actually exist. A common criterion is to

limit the water injection pressure to 1 psi/ft of borehole depth above the

water table and 0.57 psi/ft of borehole depth below the water table. This

criterion results in a maximum injection pressure less than the effective overburden pressure if the overburden has a unit weight greater than 144 lb/ft3

.

c. The coefficient of permeability, based upon laminar flow, is computed for a vertical test section with the following assumptions:

(1) Medium is homogeneous and isotropic.

(2) Laminar flow governed by Darcy's law.

(3) Radial flow from a cylindrical and vertical borehole test section

length, Radial flow implies that the equipotential surfaces form

cylinders symmetrical about the axis of the borehole test section.

(4) No inertia effects.

(5) Boundary conditions (fig. C-2).

(a) At r = ro . H = Ho .

(b) At r=R , H=0.

Where

r = radial distance from the test section (L)

ro = radius of borehole (L)

H = excess pressure head (L)

Ho = excess pressure head at the center of the test section (L) (either

measured within the test section, or computed allowing for frictional head losses within the drill pipe)

C-l
EM 1110-2-1901

30 Sep 86

R = radius of influence: radial distance from the test section

corresponding to a 100 percent loss in excess head, Ho (L)

Figure C-1. Typical water pressure test setups (prepared by WES)

C-2

{WATER FLO*) 

GROUND SURFACE 

~ z 

lLJ 

...J 

--- ~ j:: 

lJ 

lLJ 

"" IV, 

lLJ 

1-

'"-I---PACKER 

CLOSED 

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) 

PACKER 

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lJ 

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a. DOUBLE PACKER SETUP b. SINGLE PACKER SETUP 
EM 1110-2-1901

30 Sep 86

Figure C-2. Homogeneous isotropic material--radial flow

(prepared by WES)

d. Darcy's equation may be written

where

v = flow velocity (L/T)

k

e

= laminar equivalent permeability (L/T)

dh/dr = hydraulic gradient in the radial flow system (L/L)

e. The volume flow rate from the borehole cavity is

where

Q = volume flow rate (L3/T)

C-3
EM 1110-2-1901

30 Sep 86

A = area of an equipotential surface (L2

)

The area A in the radial system is

Thus

which can be written

and integrated

(C-1)

The negative sign can be dropped by choosing flow away from the borehole as

positive, thus

and the permeability is

C-4
EM 1110-2-1901

30 Sep 86

(C-2)

f. Before equation C-2 can be applied, however, the radius of influence, R , must be determined or estimated. A rough estimate of R is normally adequate since large variations in R generally produce only small

variations in the computed permeability. In equation C-2 the permeability is

directly related to the term 1n (R/r0) . The rate of change of 1n (R/ro) ,

and thus permeability, decreases rapidly as R increases. This is illustrated by considering the analysis of a pressure test conducted in an NX-size

borehole. The increase in permeability, ke (based on equation C-2), as R

is increased from 1 ft to 106 ft is shown below:

Radius of Influence,

R , ft

1

10

100

1,000

10,000

100,000

1,000,000

Equivalent Permeability,

ke , ft/sec

ke

2.1 ke

3.2 ke

4.3 ke

5.4 ke

6.5 ke

7.5 ke

Thus as R is increased from 1 ft to 106 ft, the computed permeability

increases by less than one order of magnitude. To eliminate the arbitrary

choice of R as a source of error in the permeability calculation, it has

been suggested that during a pressure test, pressure in the surrounding mass

be observed in a nearby borehole. By changing the upper limits of integration

in equation C-1 to correspond to an arbitrary distance r , within the

boundaries ro to R (fig. C-2) the following equations are developed:

Integration yields

C-5
EM 1110-2-1901

30 Sep 86

where H 1= excess pressure head at an arbitrary distance, rl , from the test

section (L) which can be written as

(C-3)

g. The coefficient of permeability, based upon nonlinear or turbulent

flow, is computed for a vertical test section in a homogeneous, isotropic

medium with the following assumptions:

(1) Medium is homogeneous and isotropic.

(2) Nonlinear or turbulent flow governed by the Missbach law

(3) Radial flow from cylindrical and vertical borehole test section of

length,

(4) No inertia effects.

(5) Boundary conditions (fig. C-2).

(a) At r = ro , H = Ho .

(b) At r=R, H=0.

h. The Missbach law may be written

where

m = degree of nonlinearity (generally between 1 and 2)

k'

e

= turbulent equivalent permeability (L/T)m

Volume flow rate for radial flow from the cavity is

C-6
EM 1110-2-1901

30 Sep 86

and it follows that:

Drop the negative sign by choosing flow away from the borehole as positive,

yielding

Equation C-4 can be rewritten as

(C-4)

(C-5)

C-7
EM 1110-2-1901

30 Sep 86

where

The logarithms of terms in equation C-5 yield the equation of a straight line:

log Ho

= log E1 + m log Q

A plot of log Ho versus log Q will be a straight line with an arithmetic

slope equal to the degree of nonlinearity m .

i. The coefficient of permeability for laminar flow in fissures is

computed for a vertical test section with the following assumptions:

(1) Vertical borehole test section of length is intersected by an

arbitrary number of horizontal fissures.

(2) Fissures are constant aperture openings between smooth parallel

plates.

(3) Radial flow occurs within each fissure and is governed by Darcy's

law. No flow occurs in material between fissures.

(4) Each fissure has the same equivalent parallel plate aperture, e .

(5) No inertia effects.

(6) Boundary conditions (fig. C-3).

(a) At r = ro , H=Ho .

(b) At r = R , H=0.

j. The derivation of equations C-6 and C-7 proceeds in the same fashion

as that given above for laminar flow through a homogeneous isotropic medium

(equations C-2 and C-3). For the fissured medium the test section length,

is replaced by the quantity (ne) where n is the number of fissures

intersecting the test section and e is the equivalent parallel plate

aperture of each fissure. The resulting expression for the flow rate Q is

C-8
EM 1110-2-1901

30 Sep 86

Figure C-3. Fissured-medium--radial flow (prepared by WES)

and the permeability of each fissure is

(C-6)

where kj = laminar fissure permeability (L/T). The general expression for

excess pressure head H1 at an arbitrary distance r1 between the boundaries

ro and R is given by

which can be written as

(C-7)

C-9
EM 1110-2-1901

30 Sep 86

From the theory of viscous flow between smooth parallel plates

(C-8)

where

Equation C-8 is substituted into equation C-6 to solve for the equivalent

parallel plate aperture, e :

k. The coefficient of permeability for nonlinear or turbulent flow in

fissures is computed for a vertical test section with the following

assumptions:

(1) Vertical borehole test section of length intersected by an

arbitrary number of horizontal fissures.

(2) Fissures are constant aperture openings between smooth parallel

plates.

(3) Radial flow occurs within each fissure and is governed by the

Missbach law (vm

 = k'i).

j

No flows occur in material between fissures.

(4) Each fissure has the same equivalent parallel plate aperture, e .

(5) No inertial effects.

(6) Boundary conditions (fig. C-3).

(a) At r = ro , H = Ho .

(b) At r=R, H=0.

1. The derivation of equation C-9 proceeds in the same fashion as that

given above for nonlinear flow through a homogeneous isotropic medium (equation C-4). For the fissured medium, the test section length, , is replaced

C-10
EM 1110-2-1901

30 Sep 86

by the quantity ne where n is the number of fissures intersecting the test

section and e is the equivalent parallel plate aperture of each fissure.

The resulting equation for the turbulent fissure permeability is

(C-9)

where k'

j

= turbulent fissure permeability (L/T)m . Equation C-9 can be

rewritten as

where

(C-10)

The logarithms of terms in equation C-10 yielded the equation of a straight

line:

A plot of log Ho versus log Q will be a straight line with an arithmetic

slope equal to the degree of nonlinearity, m .

C-2. Air Pressure Tests.

a. Air pressure tests are conducted similarly to water pressure tests,

with the essential difference being the replacement of water with air. The

use of air, however, requires that permeability equations be modified for

application to a compressible fluid and a conversion must be made from air to

water permeability. To compute the permeability, flow is assumed to be

laminar and governed by Darcy's law. The material tested is assumed to be a

homogeneous isotropic porous medium. Darcy's law can be written

v = ki

C-11
EM 1110-2-1901

30 Sep 86

where

v = flow velocity (L/T)

k = coefficient of permeability (L/T)

i = hydraulic gradient (L/L)

b. The coefficient of permeability, k , is dependent on properties of

the medium and fluid or gas. Since the test involves the flow of air and

permeability relating to the flow of water is desired, it is convenient to

solve for the intrinsic permeability, k , which is characteristic of the

medium alone. The coefficient of permeability and intrinsic permeability are

interrelated (Davis and Dewiest 1966, and Muskat 1946). For the flow of water

(C-11)

where

k

e

= laminar equivalent permeability (L/T)

= unit weight of water (F/L3)

= dynamic viscosity of water

c. The conversion of intrinsic permeability measured by an air test to

the water permeability can be in error due to differences in gas and fluid

flow phenomena i.e., the Klinkenberg Effect (Weeks 1978), or alteration of the

material's physical properties caused by a chemical reaction with the fluid or

gas (Davis and Dewiest 1966, and Lynch 1962). In sediments rich in clay

minerals, water permeability calculated from air measurements may be overestimated by a factor of 100 (Davis and Dewiest 1966). This overestimation is

caused by a hydration of clays during waterflow which does not occur during

airflow. Test results should be applied with caution as more experience and

studies are needed to determine the limitations of equation C-11.

d. Muskat (1946, p. 679) observed that the flow of incompressible

liquids is easily modified for application to the flow of a compressible gas.

Steady-state solutions for analyzing constant water pressure test results are

generally written in the form

C-12
EM 1110-2-1901

30 Sep 86

where

Q = volume flow rate (L3/T)

= length of test section (L)

Ho = excess pressure head at the center of the test section (L)

The term [C] is dependent on assumed flow and boundary conditions. The following equation is commonly used in analyzing water pressure test results.

where

R = radius of influence (L)

ro = radius of borehole (L)

After solving for Q and converting to intrinsic permeability, k ,

equation C-12 becomes

(C-12)

(C-13)

where Po = excess pressure at the center of test section (F/L2) the

equation (C-13) is based-on the assumption that:

(1) The medium is a homogeneous and isotropic porous continuum.

(2) The flow emitting from a cylindrical section of borehole is

laminar, and governed by Darcy's equation.

(3) The flow pattern is ellipsoidal and symmetrical about the axis of

the borehole test section.

e. Equation C-13 can be modified for analyzing air pressure test

results by making similar assumptions and considering the fluid to be

compressible. Before modification, equation C-13 must be written in terms of

absolute pressures. The pressure, Po , equals the absolute pressure in the

test section, minus atmospheric pressure, Equation C-13 becomes

C-13
EM 1110-2-1901

30 Sep 86

(C-14)

f. Equation C-14 is modified to apply to the flow of gas by replacing

the pressure term by the expression

where

where

is a constant at any point in the flow and defined as

(C-15)

(C-16)

= mass density (F-T2/L)/L3

g = acceleration due to gravity (L/T2

)

= absolute pressure (F/L2

)

= unit weight of gas (F/L3)

and the exponent, M , determines the thermodynamic nature of the expansion of

a gas as it moves from high- to low-pressure regions. The resulting equation

(equation C-18 below) is in terms of weight flow rate rather than volume flow

rate. Since gases are highly compressible, the volume flow rate will vary

with pressure and temperature along the flow path. However, the weight flow

rate can be assumed to remain constant. Weight flow rate,

flow rate, Q , at any point in the flow are related by

QWF , and volume

(C-17)

Substitution of expression C-15 into equation C-14 (replace μw with μa)

yields the following expression for the weight flow rate of air:

C-14
EM 1110-2-1901

30 Sep 86

(C-18)

where

QW F = weight flow rate (F/T)

μa = dynamic viscosity of air (F T/L2

)

g. For convenience, the value of M is assumed equal to 1 which corresponds to isothermal expansion of an ideal gas as it moves from the borehole

through the medium (for adiabatic expansion, M < 1). Since equation C-16 is

valid at any point in the flow and M + 1 , can be replaced by

where and are the unit weight of air and absolute pressure in the

test section, respectively. By substituting M = 1 and in

equation C-18, the intrinsic permeability, k , can be expressed as

(C-19)

h. Parameters used in equation C-19 are measured or computed from the

test data. The test section length, , and radius of test section, ro ,

are determined from the test setup.

equals 14.7 psi or 2,120 lbF/ft2.

Standard atmospheric pressure,

The absolute pressure in the test section,

is equal to the gage pressure measured in the test section, PO , plus

atmospheric pressure, The dynamic viscosity of air, μa , depends only

on the temperature, and its variation is small over a large range of temperaFor example, air viscosity increases from approximately 0.035 x 10-5

tures.

to 0.045 x 10-5 lbF-sec/ft2 as temperature increases from 0 to 250° F. In

general, the dynamic viscosity of air can be assumed to equal 0.38 x

10-5 lbF-sec/ft2

 which is the viscosity of air at 68° F.

i. The weight flow rate from the test section, QWF , is constant along

the flow path and can be determined at the manifold by applying equation C-17:

C-15
EM 1110-2-1901

30 Sep 86

where

QW F = weight flow rate (F/T)

Qm = volume flow rate at the manifold (L3/T)

= unit weight of air at the manifold (F/L3

)

The value of is related to the pressure and temperature by the equation

of state (Vennard 1965):

where

= unit weight of air at the manifold (lbF/ft3)

absolute pressure at the manifold (lbF/ft2)

R g = engineering gas constant for air (53.3 ft-lbF/lbF-degrees Rankine)

= absolute temperature at the manifold (degrees Rankine)

j. The unit weight of air in the test section, , is also computed

from the equation of state:

where = absolute temperature in test section (degrees Rankine). All the

parameters needed to compute the intrinsic permeability, k , by equation C-19

have now been determined. The equivalent permeability applicable to the flow

of water, ke , is computed by substitution of k into equation C-11 yielding

the following general equation:

C-16
EM 1110-2-1901

30 Sep 86

where

k

e

= laminar equivalent permeability (L/T)

Qm = volume flow rate at the manifold (L3/T)

= length of the test section (L)

= unit weight of water (F/L3)

μa = dynamic viscosity of air

μw = dynamic viscosity of water

= absolute temperature in test section (degrees Rankins)

= absolute pressure at the manifold (F/L2)

= absolute temperature at the manifold (degrees Rankins)

= absolute pressure in test section (F/L2)

= atmospheric pressure (F/L2)

R = radius of influence (L)

ro = radius of the borehole (L)

C-3. Pressure Holding Tests.

a. The pressure holding test, sometimes called a pressure duration or

pressure drop test, is conducted by pressurizing the test section to a known

value, then stopping the water supply and observing the rate of pressure

decay. A pressure holding test is usually conducted in conjunction with a

water pressure test. For the conduct of the test, a pressure transducer

mounted in the test section is used to provide a continuous record of pressure

versus time.

b. Tests in fissured rock can be analyzed through application of the

parallel plate analogy. The laminar fissure permeability, kj , is related to

the pressure drop data by the expression

C-17
EM 1110-2-1901

30 Sep 86

(C-20)

where

ro = radius of borehole (L)

= excess pressure head at the center of the test section at the

initiation of a pressure drop test (L)

= excess pressure head at the center of the test section at the

completion of a pressure drop test (L)

R = radius of influence (estimated) (L)

n = number of fissures intersecting the test section

tdrop = duration of the pressure drop test (T)

c. Equation C-20 was derived by Maini (1971) based on the following

assumptions.

(1) Radial flow occurs from a vertical test section and is governed by

Darcy's law.

(2) Fissure system intersecting the test section is represented by horizontal parallel plates of equal aperture and spacing.

(3) Test zone is saturated. Maini (1971) suggests that before conducting tests in zones above the ground-water table, water be pumped into the borehole test section to saturate the fissure system in the immediate vicinity of

the borehole.

d. The equivalent parallel aperture, e , in equation C-20 is unknown;

however, by parallel plate analogy

which when substituted into equation C-20 yields

(C-21)

(C-22)

C-18
EM 1110-2-1901

30 Sep 86

The aperture, e , is computed by equation C-22 and substituted into equation C-21 to obtain the permeability kj . If the test zone is modeled as

a homogeneous isotropic porous medium and assumptions (1) and (3) above are

valid, an expression for the laminar equivalent permeability, ke , is

obtained by replacing the quantity ne in equation C-20 with the length of the

test section, , to yield

(C-23)

e. The pressure drop test is a suitable supplement to the water pressure test and possesses certain advantages. The pressure drop test is likely

to require a significantly smaller volume of water than that needed in a

constant pressure test. The savings in water can be important when conducting

tests in regions with a limited water supply. The measurement of pressure in

the test section by an electric transducer allows the pressure drop test to be

conducted with low initial pressures regardless of the depth of the test

section, since the water level in the flow pipe only needs to be above the top

of the test section to initiate a test. The use of low initial pressures has

the additional advantage of reducing friction pressure losses during the conduct of a test.

C-19
APPENDIX D 

FILTER DESIGN 

EM 1110-2-1901 

30 Apr 93 

Change 1 

D-1. General. The objective of filters and drains used as seepage control 

measures for embankments is to efficiently control the movement of water 

within and about the embankment. In order to meet this objective, filters and 

drains must, for the project life and with minimum maintenance, retain the 

protected materials, allow relatively free movement of water, and have sufficient discharge capacity. EoLdesign,. these. three. necessLties are termed, 

respectively, piping or stability requirement, permeability requirement, and 

discharge capacity. This appendix will explain how these requirements are met 

for cohesionless and cohesive materials, and provide general construction 

guidance for installation of filters and drains. The terms filters and drains 

are sometimes used interchangeably. Some definitions classify filters and 

drains by function. In this case, filters must retain the protected soil and 

have a permeability greater than the protected soil but do not need to have a 

particular flow or drainage capacity since flow will be perpendicular to the 

interface between the protected soil and filter. Drains, however, while meeting the requirements of filters, must have an adequate discharge capacity 

since drains collect seepage and conduct it to a discharge point or area. In 

practice, the critical element is not definition, but recognition, by the 

designer, when a drain must collect and conduct water. In this case the drain 

must be properly designed for the expected flows. Where ic is not possible to 

meet the criteria of this appendix, che design must be cauciously done and 

based on carefully controlled laboratory filter tests (Perry 1985). 

D-2. Stability. Filters and drains< 1 l allow seepage to move out of a protected soil more quickly than the seepage moves within the protected soil. 

Thus, the filter material must be more open and have a larger grain size than 

the protected soil. Seepage from the finer soil to the filter can cause movement of the finer soil particles from the protected soil into and through the 

filter. This movement will endanger the embankment. <

2 > Destruction of the 

protected soil structure may occur due to the loss of material. Also, clogging of the filter may occur causing loss of the filter's ability to remove 

(1) 

(2) 

In paragraphs D-2 and D-3 the criteria apply to drains and filters; for 

brevity, only the word filter will be used. 

In practice, it is normal for a small amount of protected soil to move 

into the filter upon initiation of seepage. This action should quickly 

stop and may not be observed when seepage first occurs. This is one 

reason that initial operation of embankment seepage control measures 

should be closely observed by qualified personnel. 

D-1 
EM 1110-2-1901 

30 Apr 93 

Change 1 

water from the protected soil. Criteria developed by many years of experience 

are used to design filters and drains which will prevent the movement of protected soil into the filter. This criterion, called piping or stability criterion, is based on the grain·size relationship between the protected soil and 

the filter. In the following, the small character "d" is used to represent 

the grain size for the protected (or base) material and the large character 

"D" the grain size for the filter material. 

Determine filter gradation limits using the following steps:(3 l 

1. Determine the gradation curve (grain-size distribution) of the base soil 

material. Use enough samples to define the range of grain sizes for the base 

soil or soils and design the filter gradation based on the base soil that 

requires the smallest D15 size. 

2. Proceed to step 4 if the base soil contains no gravel (material larger 

than No. 4 sieve). 

3. Prepare adjusted gradation curves for base soils with particles larger 

than the No. 4 (4.75 mm) sieve. 

a. Obtain a correction factor by dividing 100 by the percent passing 

the No. 4 (4.75 mm) sieve. 

b. Multiply the percentage passing each sieve size of the base soil 

smaller than No. 4 (4.75 mm) by the correction factor from step 3a. 

c. Plot these adjusted percentages to obtain a new gradation curve. 

d. Use the adjusted curve to determine the percent passing the No. 200 

(0.075 mm) sieve in step 4. 

4. Place the base soil in a category based on the percent passing the No. 

200 (0.075 mm) sieve in accordance with Table D-1. 

5. Determine the maximum D15 size for the filter in accordance with 

Table D-2. Note that the maximum D15 is not required to be smaller than 

0.20 nun. 

6. To ensure sufficient permeability, set the m1n1mum D15 greater than or 

equal to 3 to 5 x maximum d 15 of the base soil before regrading but no less 

than 0.1 mm. 

( 3) Guide for Determining the Gradation of Sand and Gravel Filters, Soil 

Mechanics Note No. 1, U.S. Department of Agriculture Soil Conservation 

Services, Engineering Division, Jan 1986. 

D-2 
Table D-1. Categories of Base Soil Materials 

Percent Finer Than the No. 

Category (0.075 mm) Sieve 

1 >85 

2 40-85 

3 15-39 

4 <15 

EM 1110-2-1901 

30 Apr 93 

Change 1 

200 

7. Set the maximum particle size at 3 in. (75 mm) and the maximum passing the 

No. 200 (0.075 mm) sieve at 5 percent. The portion of the filter material 

passing the No. 40 (0.425 mm) sieve must have a plasticity index (PI) of zero 

when tested in accordance with EM 1110-2-1906, "Laboratory Soils Testing." 

8. Design the filter limits within the maximum and minimum values determined 

in steps 5, 6, and 7. Standard gradations may be used if desired. Plot the 

limit values, and connect all the minimum and maximum points with straight 

lines. To minimize segregation and related effects, filters should have relatively uniform grain-size distribution curves. without "gap grading"--sharp 

breaks in curvature indicating absence of certain particle sizes. This may 

require setting limits that reduce the broadness of filters within the maximum 

and minimum values determined. Sand filters with D90 less than about 20 mm 

generally do not need limitations on filter broadness to prevent segregation. 

For coarser filters and gravel zones that serve both as filters and drains, 

the ratio D90 /D10 should decrease rapidly with increasing D10 size. The limits 

in Table D-3 are suggested for preventing segregation during construction of 

these coarser filters. 

D-3 
'EM 1110-2-1901 

30 Apr 93 

Change 1 

Table D-2. Criteria for Filters 

Base 

Soil 

Category 

1 

2 

Base Soil Description, and 

Percent Finer Than No. 200 

(0.075 mm) Sieve (a) 

Fine silts and clays; 

more than 85% finer 

Sands, silts, clays, and 

silty and clayey sands; 

40 to 85% finer 

Filter Criteria (b) 

(c) D15 :,; 9 X da 5 

D15 :,; 0. 7 mm 

3 Silty and clayey sands 

and gravels; 

(d), (e) D < r 40-A) 15 - L4o rs 

4 

15 to 39% finer 

Sands and gravels; less 

than 15% finer 

[ ( 4 X d85 ) - 0 . 7 mm ] + 0 . 7 mm 

(f) D15 :,; 4 to 5 x d85 

(a) Category designation for soil containing particles larger than 4.75 mm is 

determined from a gradation curve of the base soil which has been adjusted 

to 100% passing the No. 4 (4.75 mm) sieve, 

(b) Filters are to have a maximum particle size of 3 in. (75 mm) and a maximum 

of 5% passing the No. 200 (0.075 mm) sieve with the plasticity index (PI) 

of the fines equal to zero. PI is determined on the material passing the 

No. 40 (0.425 mm) sieve in accordance with EM 1110-2-1906, "Laboratory 

Soils Testing." To ensure sufficient permeability, filters are to have a 

D15 size equal to or greater than 4 X d15 but no smaller than 0.1 mm. 

(c) When 9 X d85 is less than 0_2 mm, use 0.2 mm_ 

(d) A - percent passing the No. 200 (0.075 mm) sieve after any regrading. 

(e) When 4 X d85 is less than 0.7 mm, use 0.7 mm-

(f) In category 4, the D15 :,; 4 X d85 criterion should be used in the case of 

filters beneath riprap subject to wave action and drains which may be 

subject to violent surging and/or vibration. 

D-4 

I I 
Table D-3. 

Minimwn D10 

(mm) 

<0.5 

0.5 1.0 

1.0 2.0 

2.0 5.0 

5.0 10 

10 50 

EM 1110-2-1901 

30 Apr 93 

Change 1 

D10 and D90 Limits for Preventing Segregation 

Maximum D90 

(mm) 

20 

25 

30 

40 

50 

60 

D-3. PermeabilitY. The requirement that seepage move more quickly through 

the filter than through the protected soil (called the permeability criterion) 

is again met by a grain-size relationship criterion based on experience: 

Permeability 

15 percent size of filter material 

15 percent of the protected soil " 3 to 5 (D-1) 

Permeability of a granular soil is roughly proportional to the square of the 

10- to 15-percent size material. Thus, the permeability criterion ensures 

that filter materials have approximately 9 to 25 or more times the permeability of the protected soil. Generally, a permeability ratio of at least 5 is 

preferred; however, in the case of a wide band of uniform base material 

gradations, a permeability ratio as low as 3 may be used with respect to the 

maximum 15-percent size of the base material. There may be situations, particularly where the filter is not part of a drain, where the permeability of 

the filter is not important. In those situations, this criterion may be 

ignored. 

D-4. Applicability. The previously given filter criteria in Table D-2 and 

Equation D-1 are applicable for all soils (cohesionless or cohesive soils) 

including dispersive soils.( 4 l However, laboratory filter tests for dispersive soils, very fine silt, and very fine cohesive soils with high plastic 

limits are recommended. 

( 4) Sherard, J. L., L. P. Dunnigan, "Filters and Leakage Control in Embankment Dams," Proceeding of the Symposium on Seepage and Leakage from Dams 

and Impoundments, ASCE National Convention, Denver, Colorado, 1985. 

D-5 
EM 1110-2-1901 

30 Apr 93 

Change 1 

D-5. Perforated Pipe.C5 l The following criteria are applicable for preventing infiltration of filter material into perforated pipe, screens, etc.: 

Minimum 50 percent size of filter material 

hole diameter or slot width ;, l. 0 (D- 2) 

In many instances a filter material meeting the criteria given by Table D-2 

and Equation D-1 relative to the material being drained is too fine to meet 

the criteria given by Equation D-2. In these instances, multilayered or 

"graded" filters are required. In a graded filter each layer meets the 

requirements given by Table D-2 and Equation D-1 with respect to the pervious 

layer with the final layer in which a collector pipe is bedded also meeting 

the requirements given by Equation D-2. Graded filter systems may also be 

needed when transitioning from fine to coarse materials in a zoned embankment 

or where coarse material is required for improving the water-carrying capacity 

of the system. 

D-6. Gap-Graded Base. The preceding criteria cannot, in most instances, be 

applied directly to protect severely gap- or skip-graded soils. In a gapgraded soil such as that shown in Figure D-1, the coarse material simply 

floats in the matrix of fines. Consequently, the scattered coarse particles 

will not deter the migration of fines as they do in a well-graded material. 

For such gap-graded soils, the filter should be designed to protect the fine i. 

matrix rather than the total range of particle sizes. This is illustrated in 

Figure D-1. The 85-percent size of the total sample is 5.2 mm. Considering 

only the matrix material, the 85-percent size would be 0.1 mm resulting in a 

much finer filter material being required. This procedure may also be followed in some instances where the material being drained has a very wide range 

of particle sizes (e.g., materials graded from coarse gravels to significant 

percentages of silt or clay). For major structures such a design should be 

checked with filter tests. 

D-7. Gap-Graded Filter. A gap-graded filter material must never be specified 

or allowed since it will consist of either the coarse particles floating in 

the finer material or the fine material having no stability within the voids 

produced by the coarse material. In the former case the material may not be 

permeable enough to provide adequate drainage. The latter case is particularly dangerous since piping of the protected material can easily occur 

through the relatively large, loosely filled voids provided by the coarse 

material. 

(5) EM 1110-2-2300 states, "Collector pipe should not be placed within the 

embankment, except at the downstream toe, because of the danger of 

either breakage or separation of joints, resulting from fill placement 

and compaction operations, or settlement, which might result in either 

clogging and/or piping." 

D-6 
u .,_ ... ,.._ '"'f"' \l t. fi_,.PAM •t~ NWI:!US _,.. I 4 I I • I I ... .... .. .. " ,. 1• UIO .. r\, . 1 •• -. • -- -~--- ·+ f- -- - - - 1- - . . , .. " 1-- r-- o., o., - • ~.;. M~TfOIAL - . -I-f- - .... """ .. 7 ~- . TOTAL MATf~l.~l ~ - r---..--- • - -- - -

I -I \. . 

' - ..... -- ···- - . -- - 1- ~ -\- - - - 1- ~ 

I \ I I ~· .. ~ 

-- - .. 

' fi ' -" - ·-· - -- - ··- ~- -I-1- -- - --- -- e 

.. . - - - -·-1- . ---- - . - --I-

- .. ·- -- ~- 1-r-1- -- ~-

• .. - -. - . , __ 1- --· 1- -· --... - .. • • .. .. ... ... - . ... UWM san • .._LIN(fla 

I I ....... I ~ I •• Dill Q.Af I _,. - I ... I I - •!"" ''!" 

Figure D-1. Analysis of gap-graded material (from EM 1110-2-1913) 
EM 1110-2-1901 

30 Apr 93 

Change 1 

D-8. Broadly Graded Base. One of the more common soils used for embankment 

dams is a broadly graded material with particle sizes ranging from clay sizes 

to coarse gravels and including all intermediate sizes. These soils may be of 

glaGial, alluvial-colluvial, or weathered rock origin. As noted by Sherard, 

since the 85-percent size of the soil is commonly on the order of 20 to 30 mm, 

a direct application of the stability criteria D15jd05 :5 4 to 5 would allow 

very coarse uniform gravel without sand sizes as a downstream filter, which 

would not be satisfactory (Sherard 1979). The typical broadly graded soils 

fall in Soil Category 2 in Table D-2 and require a sand or gravelly filter 

with D15 :5 0. 7 mm. 

D-9. Example of Graded Filter Design for Drain. Seldom, if ever, is a single 

gradation curve representative of a given material. A material is generally 

represented by a gradation band which encompasses all the individual gradation 

curves. Likewise, the required gradation for the filter material is also 

given as a band. The design of a graded filter which shows the application of 

the filter criteria where the gradations are represented by bands is illustrated in Figure D-2. A typical two-layer filter for protecting an impervious 

core of a dam is illustrated. The impervious core is a fat clay (CH) with a 

trace of sand which falls in Category 1 soil in Table D-2. The criterion 

D15 :5 9 x d85 is applied and a "point a" is established in Figure D-2. Filter 

material graded within a band such as that shown for Filter A in Figure D-2 is 

acceptable based on the stability criteria. The fine limit of the band was 

arbitrarily drawn, and in this example, is intended to represent the gradation 

of a readily available material. A check is then made to ensure that the 

15-percent size of the fine limit of the filter material band (point b) is 

equal to or greater than 3 to 5 times the 15-percent size of the coarse limit 

of the drained material band (point c). Filter A has a minimum D10 size and a 

maximum D90 size such that, based on Table D-3, segregation during placement 

can be prevented. Filter A meets both the stability and permeability requirements and is a suitable filter material for protecting the impervious core 

material. The second filter, Filter B, usually is needed to transition from a 

fine filter (Filter A) to coarse materials in a zoned embankment dam. 

Filter B must meet the criteria given by Table D-2 with respect to Filter A. 

For stability, the 15-percent size of the coarse limit of the gradation band 

for the second filter (point d) cannot be greater than 4 to 5 times the 

85-percent size of the fine limit of the gradation band for Filter·A 

(point e). For permeability, the 15-percent size of the fine limit (point f) 

must be at least 3 to 5 times greater than the 15-percent size of the coarse 

limit for Filter A (point a). With points d and f established, the fine and 

coarse limits for Filter B may be established by drawing curves through the 

points approximately parallel to the respective limits for Filter A. A check 

is then made to see that the ratio of maximum D90/minimum D10 size of Filter B 

is approximately in the range as indicated in Table D-3. A well-graded filter 

which usually would not meet the requirements in Table D-3 may be used if 

segregation can be controlled during placement. Figure D-2 is intended to 

show only the principles of filter design. The design of thickness of a 

D-8 

• 

.-

( 
t:1 

' "' 

10 0 

.. 

10 

7 0 

; 50 

"' 

30 

,. 

D 

• 

U.S. STANDARD SIEVE OPENING IN INCHES U.S. STANDARD SIEVE NUMBERS HYDROMETER 

111512 10 I I 4 3 2 1¥1 1 ¥. ~ ~ 3 • I I 10 U 11 20 3D •o 50 70 100 140 2:00 

I' \ ' . ' ' ' ' . 

' "-.. 

\e D. (das) min 

11 1\ 1\ 1\ \ ' \ 

'\ \ 1\ \ " 

\ \ \ ~ ':::< " ~~ _1 .,. .. ~ ? '\ ~0.~ ~ 1\ '\.~c fP \ '-o,.., 

1\ \ 

\ \ 

\ a.;; 9 (das) min 

\ \ 

\ I ;;.3 to 5a l\ 

' \ 

I D.b b;;.3 to 5c 

al '\ --"'-

d.;; to 5e 1\ ~ 

I I I \ "" 100 .. 10 0.5 0.1 0.05 0.01 0.005 

GRAIN SIZE IN MIWMETERS 

Figure D-2. Illustration of the design of a graded filter 

''-

' 

,'\ 

~ 

D 

1 0 

20 

30 

~ 70 

'\ 

10 

C\ 

90 

100 

0.001 
EM 1110-2-1901 

30 Apr 93 

Change 1 

filter for sufficient seepage discharge capacity is done by applying Darcy's 

Law, Q - kia, and one example is presented in Chapter 8 of the main text. 

D-10. Construction. EM 1110-2-1911 and EM 1110-2-2300 provide guidance for 

construction. Major concerns during construction include: 

a. Prevention of contamination of drains and filters by runoff containing sediment, dust, construction traffic, and mixing with nearby fine-grained 

materials during placement and compaction. Drain and filter material may be 

kept at an elevation higher than the surrounding fine-grained materials during 

construction to prevent-contamination by sediment-carrying runoff. 

b. Prevention of segregation, particularly well-graded filters, during 

handling and placement. 

c. Proper in-place density is usually required to be an average of 

85-percent relative density with no area less than SO-percent relative 

density. Granular materials containing little or no fines should be saturated 

during compaction to prevent "bulking" (low density) which can result in 

settlement when overburden materials are placed and the drain is subsequently 

saturated by seepage flows. 

d. Gradation should be monitored closely so that designed filter cri- •.' ~ 

teria are met. 

e. Thickness of layers should be monitored to ensure designed discharge 

capacity and continuity of the filter. 

Thus, quality control/assurance is very important during filter construction 

because of the critical function of this relatively small part of the 

embankment. 

D-11. Monitoring. Monitoring of seepage quantity and quality (see Chapter 13 

for method of monitoring seepage) once the filter is functioning is very 

important to the safety of the embankment. An increase in seepage flow may be 

due to a higher reservoir level or may be caused by cracking or piping. The 

source of the additional seepage should be determined and action taken as 

required (Chapters 12, 13, and 14). Decreases in seepage flows may also signal dangers such as clogging of the drain(s) with piped material, iron oxide, 

calcareous material, and effects of remedial grouting. Again, the cause 

should be determined and appropriate remedial measures taken. Drain outlets 

should be kept free of sediment and vegetation. In cold climates, design or 

maintenance measures should be taken to prevent clogging of drain outlets by 

ice. 

D-10 

•